PII: 0898-1221(89)90264-2 Computers Math. Applic. Vol. 17, No. 4 - 6 , pp. 837-885, 1989 0097-4943/89 $ 3 . 0 0 + 0 . 0 0 Printed in Great Britain. All rights reserved Copyright © 1989 Pergamon Press pie S Y M M E T R Y A S P E C T S O F B O O K B I N D I N G S M. ROZSONDAI Department o f Manuscripts and Rare Books, Library o f the Hungarian Academy o f Sciences, P.O. Box 7, Budapest, H-1361, Hungary B. R O Z S O m ) A I Structural Chemistry Research Group o f the Hungarian Academy o f Sciences, E6tv6s University, P.O. Box 117, Budapest, H-1431, Hungary Abstract--Geometric and other relations of decorated leather bookbindings are analysed. Symmetry properties o f the ornamentation, the symmetries o f motifs and o f the layout, and some correlations o f symbols and ideas, furthermore the occurrence o f one- and two-dimensional space groups and interlace designs are demonstrated by Romanesque and Gothic bindings, Hungarian, Italian, French and German Renaissance, as well as by Baroque and rococo bindings, and finally, by some pieces o f modern bookbinding art. I N T R O D U C T I O N "Numero pondere et mensura Deus omnia condidit"--"God created everything by number, weight and measure." Isaac Newton dedicated these words (Fig. 1), his "tessera", to a Hungarian student, Ferenc Pfiriz Pfipai Jr, the possessor o f the album held by the Department o f Manuscripts and Rare Books o f the Library o f the Hungarian Academy o f Sciences [1]. The Academy, now embracing all branches o f knowledge from arts and humanities through natural sciences to applied sciences, was Filg. 1. Isaac Newton's autograph in the Library o f the Hungarian Academy o f Sciences. [Shelf-number: T~rt. napl6k, kis 8 ° 6.] Reproduced by permission. The authors are grateful for the kind permission to reproduce material from the holdings o f the Library o f the Hungarian Academy o f Sciences (abbreviated hereafter in figure captions as Bibl. Acad. Budapest; no special mention of the permission will be made). CA~VA 17/,~--X 837 838 M. ROZSONDAI and B. ROZSONDAI f o u n d e d in 1825 as a " L e a r n e d Society" to p r o m o t e a b o v e all H u n g a r i a n language an d literature. Thus, in addition to scientific b o o k s and periodicals, the L i b r a r y contains literary m o n u m e n t s and bequests, manuscripts and rare books. M o s t o f o u r examples o f b o o k b i n d i n g decorations will be taken f r o m there. Jan A m o s K o m e n s k ~ (Comenius), the Czech ed u cat o r, w h o f o u n d e d m o d e r n visual teaching by his most r e n o w n e d work, Orbis Sensualium Pictus (The Visible W o r m in Pictures, N u r e m b e r g 1658; L o n d o n 1659) [2], set up the ideal o f pansoph i a, a unified science reflecting the indivisibility o f nature. His b o o k , which he d r a f t e d during his stay (1648-1654) in Sfirospatak, H u n g a r y , is also a realization o f these ideas in teaching Latin and o t h e r foreign languages. It contains a passage on "Bibiliopegus, the B o o k - b i n d e r " , as well as others o n "P ri n t i n g , the Book-sellars Shop, a Book, an d a School". Recalling N e w t o n ' s maxim, one o f the striking manifestations o f measure = r6 p ~ p o v is s y m m e t r y as it appears in nature a n d in m a n ' s work. It m a y also be a bridge, as the present an d a previous special issue o f this j o u r n a l exemplify, between different fields o f artistic an d scientific h u m a n activities. In the following discussion we try to investigate geometric a n d a n a l o g o u s relations t h r o u g h o u t the history o f b o o k b i n d i n g decoration. N o a t t e m p t has been m a d e to give a complete representation o f all periods and styles; the selection o f examples was influenced by o u r personal interest and the accessibility o f material. One o f the conspicuous geometrical relations is symmetry. Point groups an d space g ro u p s will be used here to classify s y m m e t r y properties o f o r n a m e n t s b u t n o knowledge o f the t h e o r y is assumed. A point g r o u p (with the properties o f a m a t h e m a t i c a l g ro u p ) is a set o f s y m m e t r y operations, which leave at least one point o f the object fixed in space. F o r the p l an ar figures to be discussed, the s y m m e t r y o p e r a t i o n s include reflection t h r o u g h a plane (m i rro r plane, m ) a n d r o t a t i o n a b o u t an axis (two-, three-, f o u r - f o l d etc. axis, 2, 3, 4 . . . . or, in o t h e r n o t a t i o n , C2, C3, C4 . . . . ). M i r r o r planes and r o t a t i o n axes are p e r p e n d i c u l a r to the plane o f the figure. C o n v e n t i o n a l n o t a t i o n s o f s y m m e t r y groups indicate the basic s y m m e t r y o p erat i o n s o f the group. In the case o f space groups, additional s y m m e t r y o p e r a t i o n s are translation an d glide reflection, i.e. a reflection c o m b i n e d with a translation. A space g r o u p applies to an infinite lattice o r periodic p at t ern , a n d when we speak o f the one- o r two-dimensional space-group s y m m e t r y o f a decorative p at t ern , we regard it as a section o f an infinite structure. F o r t h at matter, imposing geometrical relations such as congruence, s y m m e t r y or similarity on real objects is m o r e o r less an a p p r o x i m a t i o n . Deviations f r o m exact relations are m o r e a p p a r e n t o n han d i craft p r o d u c t s - - h i s t o r i c a l b o o k b i n d i n g s typically belong to this c a t e g o r y - - a n d the extent o f deviations depends o n several factors such as technique, craftsmanship, tools and material used. Sometimes a deviation can be intentional. Stone, wood, clay tablets, p a r c h m e n t or p a p y r u s scrolls b o r e written records in ancient times before the b o o k in its present f o r m appeared. Its p r e c u r s o r was the diptych, a pair o f ivory tablets or w o o d e n boards, possibly decorated, p r o t e c t i n g the inscription in wax inside. Some folded p a r c h m e n t sheets were then placed, later also fastened, between the p a n e l s - - a n d thus the b o o k was born! All the essential elements t h a t constitute a b o o k t o d a y h ad been b r o u g h t together b y the d aw n o f the Middle Ages. A h a n d w r i t t e n a n d illuminated b o o k was itself a great asset; ivory o r precious metal covers a n d jewels a d d e d to its value and impressiveness [3]. Even in recent centuries jewelled or ivory bindings have been occasionally a p p l i e d to special o r ceremonial books. Yet the b o o k b i n d e r ' s c r a f t s m a n s h i p finds its p r o p e r expression in the p r e p a r a t i o n an d embellish- ment o f leather bookbindings. L e a t h e r h a d been a favourite material fo r covering b o o k s f r o m the early Coptic bindings until the age o f large-scale b o o k p r o d u c t i o n when the c h e a p e r binding materials o f cloth and p a p e r replaced it, at least partially. L e a t h e r bindings were most c o m m o n l y d e c o r a t e d by means o f finishing tools, each having an engraved design on its face and p r o d u c i n g a c o r r e s p o n d i n g blind or gold-tooled impression o n the leather. A pallet or fillet was used to impress a line o r parallel lines, a smaller stamp to have a unit motif. T h e roll, a tool with a brass wheel, with an engraved p a t t e r n o n its circumference, a n d the panel, a larger block o f metal, were in general use f r o m the fifteenth to the nineteenth century. T h e tool itself and its impression are d e n o t e d by the same words, viz. a stamp, a roll, a panel. A simple technique o f r e p r o d u c i n g an impressed m o t i f o r design o f a b o o k b i n d i n g is to p u t a piece o f p a p e r on it and r u b it with various soft lead pencils. Symmetry aspects of bookbindings 839 Even after the invention o f printing in the 1450s, when hundreds and hundreds o f identical copies o f an edition were produced, hand bookbinding transformed each copy into a unique entity. The purchaser and user had the b o o k bound in most cases. Bookbinding research, which grew out of bibliophilic interests in the last century, goes into the details o f the "when, where, by whom, for w h o m " etc. o f a b o o k and its binding, and, relying on the exact identification o f tools used for decoration, on owners' notes in the book, on fragmental pages used as auxiliary material in binding, on archival sources etc., has become a complex field o f study. Decorated bookbindings reveal a lot about the books and the culture o f a given age. B O O K B I N D I N G IN THE M I D D L E AGES Some Coptic leather bindings from Egypt have come down to us [4] from the sixth to the eighth centuries but such bindings existed in earlier centuries. In Europe the earliest leather bindings date from the Carolingian age (ninth and tenth centuries). These are followed by the books bound in Romanesque style (twelfth and thirteenth centuries). 139 such bindings are recorded today [5], and they represent a fully developed art o f book decoration. It must be remembered that at the time o f the Romanesque bindings, Gothic art was flourishing and dominating in the architecture o f Europe [6], and the same intellectual trend, Scholasticism, influenced bookbindings and architecture alike. Applied arts--including bookbinding--are in general characterized by a certain delay in relation to fine arts. Romanesque bindings, i.e. their layout (Fig. 2), are related rather to Coptic or Islamic bindings than to those o f the Carolingian and Ottonian ages. The transition from Romanesque to Gothic bindings is, however, quite continuous. Motifs are similar, and even the recutting o f some Romanesque tools, especially palmetto and dragon stamps has been noted [7]. The most frequent Romanesque and Gothic stamps (Fig. 3) represent lily (fleur-de-lis), palmetto, foliation, rosette (four, five and sixpetalous), birds, a pair o f birds, deer, dragon, eagle, double- headed eagle, griffin, the Holy Lamb, mermaid, monkey, pelican (the Christ-symbol), unicorn, and the symbols o f the four Evangelists (Matthew, Mark, Luke and John: angel, lion, ox and eagle). On Romanesque bindings usually there are many stamps, certainly more than on Gothic bindings. Only eight kinds o f stamps (Fig. 5) but altogether more than 600 (!) impressions o f them figure on the upper and lower cover o f the early Gothic leather binding o f a parchment codex from the fourteenth century (Fig. 4). The proper Gothic binding shows a looser layout and a much smaller number o f repetitions o f the stamps. Bilateral symmetry of motifs (Fig. 3) (point group m or Cs) and rotations with mirror planes (point groups 3m, 4mm, 5mm and 6mm or C3v, C4v, Csv and C6~, subscript v for vertical) are common, but pure rotational symmetry (point groups 2, 3, 4, . . . or C2, (?3, Ca . . . . ) is rarely applied. A playful collection o f symmetries appears on a roll (Fig. 6), including point group C3 with Fig. 2. Layout of three Romanesque bindings after [5], Nos 1, 7, 13. 840 M. ROZSONDAI and B. ROZSONDAI Fig. 3. Stamps from some Gothic bindings of the Bibl. Acad. Budapest. Symmetry aspects of bookbindings 841 Fig. 4. Early Gothic leather binding, upper cover. National Sz6ch6nyi Library, Budapest: Clmae 79. Reproduced by permission. Fig. 5. Stamps on the binding in Fig. 4: pair of birds, doubleheaded eagle, the Holy Lamb, pelican, deer, dog, monkey, bird. Fig. 6. A roll from a Gothic binding made in Augsburg. The motifs have C4v, C4v, C3, C3v, C6v, C4v, C6v, C4v, C5~ and C4v point-group symmetry, respectively. Bibl. Acad. Budapest: Rfith 1058. This roll is identical with that in Ref. [8, Plate 171, 6]. 842 M. ROZSOND~ and B. ROZSONDAI Fig. 7. Hatched motifs from Gothic bindings. Bibl. Acad. Budapest: Inc. 192, Inc. 668. a three-fold rotation axis. Asymmetric motifs are often confined to a symmetric planar figure like a circle, a lozenge, or a square, and the encircling line is also shown. Hatched motifs (Fig. 7) can be considered to possess colour symmetry, which means a combina- tion o f a geometrical synunetry operation (reflection, rotation, translation etc.) with a simultaneous permutation of colours. The use of hatching to indicate colours in heraldry explains the name "fer azur6" (azured tool) o f the hatched stamps introduced in the sixteenth century on French Renaissance bindings. I J a b c d e f g h i j I n Fig. 8. Some Gothic headed outline stamps (a-k) and two blocks (1, m) derived from them. Bibl. Acad. Budapest. The complemental space between stamps k gives the popular "cloud" pattern [9]. Symmetry aspects of bookbindings 843 Fig. 9. Gothic binding from a workshop in Herzogenburg (Ref. [8, Plate 27]). Bibl. Acad. Budapest: Inc. 534, The headed outline or cusped edge stamps (Kopfstempel in German) played an important role in the decoration of leather bindings (Fig. 8). The central field of the upper cover, within the borders, was decorated with curved branches, with a repeated vine-like tooling, especially in the southern parts of Germany (Fig. 9). This pattern became popular in Austria, Bohemia and Hungary, and it is a good example of technical progress as demanded by the increasing book production. In the 1470s a whole curved diamond-shaped compartment (Fig. 9) was circumscribed in twelve steps by impressing eight double-headed cusped edge stamps [Fig. 8(a)] and four stamps with two "heads" on the opposite sides [Fig. 8(b)]. A large number of operations was needed to fill the central panel. To accelerate the working process, a half curved branch was engraved in the tool [Fig. 8.(1)], and the bookbinder obtained a whole curved lozenge in two actions. Soon after the panel with all the details engraved was introduced [Fig. 8(m)]. The half curved branches began a new life on some Renaissance bindings in the early sixteenth century, and they appeared as ogee branches (Fig. 10). 844 M. R o z s o ~ a a n d B. Rozsol, n~^I Fig. 10. Early Renaissance binding with ogee pattern, lower cover, from a secular workshop in Buda [10]. Bibl. Acad. Budapest: Inc. 877. The cuir cisel6, i.e. the cut-leather bindings make up a special group o f Gothic bindings [11]. The outline o f the pattern is cut into the dampened leather and is emphasized by punching (stippling) the background by a pointed tool (Fig. 11). This embellishmen t required skilful masters. A similar appearance could be reached more simply by the ingenious use o f the cusped edge stamp. The master had to choose the most suitable stamps to get an indented outline o f an oak leaf (Fig. 12), or he had to think over carefully the proportions and the distances between the headed outline tools (Fig. 13). Thus, he achieved a turnover of foreground and background, and a good appearance of the oak leaf or of a four-leaved fleuron. The impressed curved lines mark the nervure o f the leaf. The upper cover o f Gothic bindings shows a more abundant ornamentation than the lower cover (Fig. 14). One or two borders, marked out by fillets, surround a central field, which is then Symmetry aspects of bookbindings 845 Fig. 1 I. Cut-leather binding, Germany, fifteenth century [11, item 62]. National Szrehrnyi Library, Budapest: Clmae 74. Reproduced by permission. subdivided by oblique straight lines to form a diamond pattern (Fig. 15), or by an arched vine-like network into curvilinear compartments (Fig. 9). While rectangular or rather square, semicircular and quadrant subfields were preferred on Romanesque bindings (see Fig. 2), resembling structures o f Romanesque architecture, perpendicular crossings o f lines were avoided in the central field o f Gothic bindings. The central rectangle is subdivided only by its main diagonals (Fig. 12), or, more often, by additional lines parallel to them (Fig. 16). On the binding in Fig. 15, the short sides o f the rectangle are divided into two sections, the long sides into three sections by intersecting lines, while the main diagonals do not appear in the pattern. Using the latter and, consequently, an equal number o f divisions on the sides o f the rectangle, would have produced too slim diamonds. In all these cases, the original C2v point-group symmetry o f the rectangle, with two mirror planes and a two-fold rotation axis perpendicular to the plane o f the figure, is retained if we disregard the pattern within the subfields. An interesting skewly oriented quasi-diamond tiling is shown in Fig. 13. The minor discrepancy between the two sides o f the rhomboid is emphasized by the alignment o f one and two cusped edge stamps along them, respectively. The symmetries o f a field and o f the motifs which fill it often disagree. A pentamerous rosette can sit in the centre o f a diamond (Fig. 15). The half diamonds along the sides o f the central rectangle contain different motifs. The foliage on the binding in Fig. 14(b) breaks through the rigid frames o f the rectangle and has four-fold rotational symmetry, point group C4. Figure 17 shows a naturally simple arrangement o f alternating drop-shape figures, all pointing downwards in the central field with the antlers in this unnatural orientation, and outgrowing the corner boxes. Adjoining single stamps in the inner border take the shape o f a tracery so characteristic o f Gothic architecture and decorative art. David's six-pointed star (Solomon's seal) in the outer corners encloses a pentapetalous flower. Bearing in mind that a rosette is the Virgin Mary's symbol, is this a hint at her line o f descent? 846 M. ROZSONDAI and B. ROZSOSDAI Fig. 12. German Gothic binding with leaf relief obtained by the headed outline tools in Fig. 8(h-j). Monastery bindery, Aldersbach, Bayern. Bibl. Acad. Budapest: Inc. 746. Symmetry aspects of bookbindings 847 Fig. 13. Gothic leaf-relief binding. Probably Ingolstadt. National Sz6ch6nyi Library, Budapest: Clmae 223. Reproduced by permission. 848 M. R o z s o ~ A I and B. Rozsom>xl a~ 0~ Z 8 t.. o Symmetry aspects of bookbindings 849 Fig. 15. Monastery binding from Vienna [12]. Bibl. Acad. Budapest: Inc. 148. 850 M.R.OZSONDAI and B. ROZ.'.'.'.'.'.'.'.'.'K)NDAI Fig. 16. Monastery binding from Weddern near Diilmen [13]. Pelbartus de Themeswar: Pomerium sermonum de sanctis. H. Gran, Hagenau (1520). Bibl. Aead. Budapest: RM III 93. A s y m m e t r y o f ideas a n d persons is represented on a simply decorated lower cover (Fig. 16) by the images o f Christ's suffering in the shields (two hands, two feet, three nails, a heart a n d spear), the names o f Jesus, his m o t h e r M a r y a n d her symbol the rosette beneath, a n d John, the disciple w h o m he loved and who stood with M a r y by his cross, a n d the symbols in the corners and h a l f d i a m o n d s o f the four Evangelists who told the story o f the Passion. A binding decorated with the same tools is kept in the British Library [14]. The edges o f a binding, and sometimes its central field too, are decorated by "frieze" patterns. The seven possible symmetries o f infinitely repeating patterns, the one-dimensional space groups have been nicely illustrated by H u n g a r i a n needlework [15]. Similarly, border patterns from book- bindings are shown in Fig. 18, and classified according to symmetry groups. (See e.g. Ref. [17] for n o t a t i o n and explanation.) Such patterns were produced either by repeated impressions o f single Symmetry aspects of bookbindings 851 Fig. 17. Gothic binding from Ulm [13]. Bibl. Acad. Budapest: Rfith F 1065. stamps [as most o f the patterns in Fig. 18 and the " c l o u d " pattern in Fig. 8(k)] or, especially later, on Renaissance bindings, by a roll. The period o f the design, i.e. the shortest distance at which the m o t i f recurs, shows the dimensions, the perimeter o f the roll (Fig. 19), or, rather with geometric ornaments, the same m o t i f is repeatedly engraved in the' periphery, and it is difficult to find o u t the true dimensions o f the tool. The floral curls i n F i g . 18(b) fit roughly in space group lg, while there exist actually at least four variants o f flowers a n d birds, and translation remains the only symmetry operation. While searching for a n d selecting from examples o f space groups o f border designs occurring on bookbindings, one m a y reflect u p o n h o w and w h y symmetries o f o r n a m e n t s were chosen, preferred or neglected. The conventions o f the given style, its stock o f forms a n d motifs seem to be decisive. 852 M. ROZ$ONDAI and B. ROZSONDAI (o) 11 lg (c) 12 (d) ml Fig. 18(a)-(d) Symmetry aspects of bookbindings 853 lm rng ITIm Fig. 18. Border patterns from Gothic ((3) and Renaissance (R) bindings [16], and their one-dimensional space groups. ---, translation vector, - - reflection plane, ---- glide reflection plane, 0 two-fold rotation axis. (a) Monastery bindery Buda (G)-Dominican bindery Vienna (G); (b) both from Augsburg (G); (c) both from Vienna (G); (d) Vienna (G)-Vienna (R); (e) Buda (R)-Venice (R); (f) Florence (R)-Minden, Germany (G); (g) Bamberg (G)--Spanish (R). Bibl. Acad. Budapest. G o t h i c figures o f animals, birds etc. or a hunting scene (Fig. 19), all viewed f r o m the side, present n o s y m m e t r y at all, a n d the simple repetition o f these motifs in a strip leads to space g r o u p 11 [Figs 18(a) and 19]. O t h e r a r r a n g e m e n t s with f u r t h e r s y m m e t r y elements are n o t likely to occur, because it rarely ha ppe ns tha t an o r d i n a r y animal is represented upside down; a nice d r a g o n , however, m a y be an e xc e pti on (Fig. 20)! B o o k b i n d e r s o f the Renaissance, however, rejected such restrictions when they impressed a roll h o r i z o n t a l l y along the edges o f the c o v e r with p o r t r a i t s or m y t h o l o g i c a l a n d allegorical figures. W e have n o t met with a h e a d - t o - h e a d tail-to-tail alignment o f animals m a k i n g up s y m m e t r y g r o u p ml. A t a n y rate, a m i r r o r plane or a glide reflection plane in an a r r a n g e m e n t o f a symme t ri c motifs, when realized by single stamps, would require b o t h " e n a n t i o m e r s ' " ( m i r r o r image copies) o f the tool. Flowers, foliage, vine o r geometrical f or ms offer a wider variety o f symmetries o f either the m o t i f itself or the p a t t e r n it comprises. CAMWA 17/4-6--Y 854 M. ROZSONDAI and B. ROZSONDA1 Fig. 19. Rolls with hunting scenes on late Gothic bindings from Augsburg (the upper three) and Memmingen (below) [16]. Bibl. Acad. Budapest. • a ' 8 o t , • • : o I • . Fig. 20. Dragon stamps forming a border design, space group 12. Drawing by Eva Kovfics-Rozsondai after Ref. [18]. Masters o f R o m a n e s q u e a n d G o t h i c b o o k b i n d i n g s obviously did n o t speculate a b o u t symmetry, they just applied it intuitively. T h e spirit o f their age, the object o f their artistic e n d e a v o u r , i.e. the b o o k cover, a n d the n a t u r e o f their materials and tools d e t e r m i n e d their work. T h e symmetries o f general layout, pa tt e rns covering fields a n d motifs m a k i n g up patter ns d o n o t necessarily har monize, and thus the resulting c omple t e d e c o r a t i o n m a y have a lower s y m m e t r y t h a n its c o m p o n e n t s , or even n o s y m m e t r y at all. R E N A I S S A N C E B O O K B I N D I N G S While the G o t h i c style is international a n d its general criteria are the same all o v e r E u r o p e , the Renaissance has n a t i o n a l ma rks, a n d these are characteristic o f the c o u n t r y whose " m a k e " the given binding is. T h e b o o k b i n d i n g s to the s outh o f the Alps differ considerably f r o m those o f the T r a n s a l p i n e area. E v e r y o n e w h o is f o n d o f beautiful b o o k s mus t have h e a r d o f the Cor vinus bindings. T h e once f a m o u s library o f the H u n g a r i a n king M atthias Cor vinus (1458-1490) held a b o u t 2000 codices [19]. A p p r o x i m a t e l y o n e - t e n t h o f the stock has survived, scattered t h r o u g h o u t 44 towns in 14 countries. T h e r e are 47 Corvi nus ma nusc ri pt s a nd 3 i n c u n a b u l a t t o d a y in H u n g a r y . S ome o f the b o o k s have their original silk, velvet o r c o l o u r e d gold-tooled leather bindings. T h e u p p e r a n d lower covers o f the d e c o r a t e d leather bindings are identical, a p a r t f r o m the title o r the a u t h o r ' s name, impressed at the t o p o f the lower cover. Italian Renaissance a n d oriental influences are mixed with local decorating t r a d i t i o n o n these typically H u n g a r i a n p r o d u c t s (Fig. 21). T h e floral motifs: rosette, calyx-flower, leaves, peltate, p a l m e t t o s a nd tulips are in general gilded, the cablework is blind, the tBooks printed in the fifteenth century. Symmetry aspects of bookbindings 855 ¢D J ¢ N oh 856 M. ROZSONDAI and B. ROZSONDAI (cJ) ) ) 0 Fig. 21. Gold-tooled Corvinus bindings. (a) Osterreichische Nationalbibliothek (ONB): Cod. Lat. 1037. (b) National Sz6ch6nyi Library, Budapest: Clmae 422. (c) ONB: Cod. Lat. 1391. Reproduced by permission. (d) Schemes of the central designs after Ref. [20]. punch dotting coloured. Either the royal coat o f arms or Matthias' raven (corvus in Latin, hence his epithet) is placed in the centre. A m o n g the extant copies one c a n n o t find two identically decorated bindings. The overall symmetry is quite simple, C2v, except for some details. An interesting feature o f the large n u m b e r o f emphasized central panels has been noted [20], a leap o f a form into its negative, an interconversion o f figure and its background. All these forms can be imagined as enclosures shaped by surrounding copies o f one and the same m o t i f [Fig. 21 (d)], which by itself also appears as a central piece. The figure/background effect is even more p r o n o u n c e d in the repeated pattern o f Fig. 22, which was obviously inspired by a certain type o f oriental carpet (Fig. 23). Some tools o f the Corvinus bindings, first o f all the flower-cup, were recut and used in other binderies in Buda in the first three decades o f the sixteenth century. In addition, new stamps and rolls were produced (Fig. 24), and a m o n g them the different interlaced k n o t w o r k motifs and the rolls combining palmettos with leaves o f the acanthus became extremely popular. A n u m b e r o f their variants existed [Fig. 25(a)] on H u n g a r i a n Renaissance bindings. The acanthus leaves were a c o m m o n o r n a m e n t a t i o n in Greek architecture in the fifth century B.C. and revived in the fifteenth and sixteenth centuries all over Europe [Fig. 25(b), (c)]. The interlace or strapwork also occurs in architecture (Fig. 26). Italian Renaissance bindings are lightly decorated and pleasantly spaced out. A large scale o f k n o t w o r k stamps, arabesque centrepieces, linked arabesque circles as borders are their most prominent stylistic features (Figs 27, 28). Coptic and Islamic motifs as well as Persian elements like the peas-trailer or clasper can be recognized on them (Fig. 29). Different types o f Renaissance bindings developed in France in the sixteenth century. A n u m b e r o f the books b o u n d for Jean Grolier, the bibliophile, were decorated by complicated interlace work (Fig. 30). A n o t h e r trend o f b o o k o r n a m e n t a t i o n , which was connected with the French royal court and h a d remained in practice well into the seventeenth century, created elegant masterpieces by simpler geometrical means. These sem6 bindings (semer = to sow) provide an o p p o r t u n i t y to demonstrate two-dimensional space groups. Only some o f the 17 possible two-dimensional space groups occur on bookbindings. The continuity o f the pattern is broken n o t only by field boundaries but also by variant or extrinsic elements o f decoration, a n d the n u m b e r o f repetitions o f the basic m o t i f or tile is too small to speak o f an "infinitely repeating" pattern. On a sem6 binding, the lattice points, in which the motifs are placed, Fig. 22. Gold-tooled Corvinus binding with repeated pattern. Osterreichische Nationalbibliothek: Cod. Lat. 2271. Reproduced by permission. Fig. 23. Holbein-carpet. Anatolia, sixteenth century. 150 x 220 cm. Museum of Applied Arts, Budapest: Inv. 14785. Reproduced by permission. 858 M. ROZSO~rDAI and B. ROZaONDAI Fig. 24. Hungarian Renaissance binding [21] of the so-called Virginia Codex, a Hungarian linguistic record. Franciscan monastery, Buda, 1510-1522. Bibl. Acad. Budapest: K 40. Symmetry aspects of bookbindings 859 (a) Fig. 25.(a) Rolls of palmettos and acanthus leaves from Hungarian Renaissance bindings. (b) Frieze from the Erechtheion, Acropolis, Athens. (c) Pilaster head from king Matthias' palace, Buda. 860 M. ROZSONOA~ and B. RO7_..qONDAI (b) (a) ~ 7 Fig, 26.(a) Knotwork border design composed of single stamps from the Hungarian Renaissance binding: Bibl. Acad. Budapest: Inc. 1018. (b) A five-strand knotwork frieze in the town-hall yard of Trogir, Yugoslavia. (o) (b) Fig. 27. Italian Renaissance bindings, sixteenth century, with different types ofknotwork (a), and arabesque circle border (b). Bibl. Acad. Budapest: K 394, Ant. 195. Symmetry aspects of bookbindings 861 Fig. 28. Arabesque centre and corner pieces. Bibl. Acad. Budapest: Ant. 899, RM IV F 164. Fig. 29. Gold-tooled Renaissance binding. Venice [22, 23]. National Sz6ch6nyi Library, Budapest: Clmae 313. Reproduced by permission. 862 M. ROZSONDAI and B. ROZSONDAI Fig. 30. French Renaissance binding for Jean Grolier [23, Plate 116]. Osterreichische Nationalbibliothek: 73.E.20 (ES 191). Reproduced by permission. form a rectangular (space group pmm, see Ref. [17] for notation) or a diamond tiling (cmm) (Fig. 31). The symmetry o f the pattern is then determined by the symmetry o f the underlying motif and the lattice. The fleur-de-lis motifs in a lozenge-type arrangement (Fig. 32) form a pattern with symmetry cm (Fig. 31). A system o f alternating motifs is a superposition o f two or more lattices (Fig. 33). Although this array has a low geometrical symmetry, it possesses further symmetry elements that include permutations o f the motifs. This is then a case o f colour symmetry, with the motifs representing the different colours. The Gothic diamond tiling (Figs 15 and 16) and the analogous vine-like diaper (Fig. 9) also belong to space group cram (Fig. 31). The binding from the Corvinian Library (Fig. 22) has a higher tetragonal symmetry p4m (Fig. 34) if the details and the layering o f the interlace work are disregarded. A much wider variety o f space groups and colour groups occurs on decorated papers used as b o o k covers or lining [24] or as wallpaper. The symmetry o f an interlace pattern can be studied at different levels. First, we may regard the pattern as a composition o f lines and figures in the plane they decorate, exactly as it appears, disregarding its three-dimensional appearance. The two interlaced square frames in Fig. 35 thus possess only an eight-fold rotation axis but no mirror planes (point group Cs). This figure can also V v p m m c m m c m Fig. 31. Two-dimensional space groups o f the rectangular (pmm) and the lozenge (cram) lattice, and a lozenge-type array (cm) o f motifs with C, point-group symmetry. O and V motifs, - - reflection plane, . . . . glide reflection plane, | two-fold rotation axis. Symmetry aspects o f bookbindings 863 Fig. 32. Sem6 binding, first half o f the seventeenth century, probably from the Netherlands. Museum o f Applied Arts, Budapest: Inv. 51.86. Reproduced by permission. be regarded as an eight-pointed star, with "hidden" parts o f the strips added. N o w it has eight reflection planes in addition to the eight-fold axis (point group Csv). A third way o f looking at the figure is to consider its two or more layers and introduce symmetry operations such as a combination o f reflection with a permutation o f layers. Geometric and such combined symmetry operations make up the layer groups. The double-square m o t i f (Fig. 35) can be regarded as lying in a two-sided plane, or it can simply be characterized as a three-dimensional object o f point-group Fig. 33. Pattern, space group p l , composed o f double letters M and Y, tears and flames on a sem6 binding. Sketch after Ref. [4, Plate 93]. ~s' s Sj % i f .s p4m Fig. 34. Symmetry elements o f the two-dimensional space group p4m. See Fig. 31 for notation, and • four-fold rotation axis. 864 M. ROZSONDAI and B. ROZSONDAI Fig. 35. Interlace m o t i f from a Renaissance binding. Venice. Bibl. Acad. Budapest: R M IV F 164. Fig. 36. Italian-type Renaissance binding, middle of the sixteenth century. Bibl. Acad. Budapest: Ant. 833. Symmetry aspects of bookbindings 865 Fig. 37. Portraits of Luther a n d M e l a n c h t h o n o n the central panels of upper and lower cover, respectively, of the binding by Thomas Kruger, Wittenberg, 1571 [25]. Novum Testamentum. Interpreted by Th. Beza. H. Stephanus, Genevae (1567). Bibl. Acad. Budapest: 542.338. symmetry Ds, with an eight-fold axis and eight two-fold axes perpendicular to it. Further examples of layered motifs and patterns are shown in Figs 18(c), 27(a), 30, 36 and 54. On bookbindings, a braid of continuous strands or an interlace of loops and strands is often simulated by single stamps [Fig. 26(a)], and imperfections at the linkages may make an exact evaluation of the structure difficult. The four-strand knotwork in Fig. 18(c) (upper) is obtained by two single stamps: one straight, one curved. Note the different slopes of the ascending and descending branches, giving serrated rather than symmetric wave lines. In the countries north of the Alps panels and rolls dominate on Renaissance bookbindings. Both have mainly figural decorations, a portrait or a scene from the Holy Bible etc. The upper and lower covers are almost the same, except for the central panels, which, however, are related conceptually. Thus, if leaders of the Protestant Reformation are shown, Luther is accompanied by Melanchthon (Fig. 37), Calvin by B6ze, and if a "Reformer roll" is used we can nearly always see the following four portraits: Martin Luther, Johann Hus, Erasmus Rotterdamus and Philipp Melanchthon ( = M a r t i - I o h a n - E r a s R-Phi Me: Fig. 38). Personified virtues such as Justitia, Fortuna (Fig. 39), Fides (faith), Spes (hope), Caritas (Christian love), Patientia, Prudentia (prudence and providence), Fortitudo (strength of mind, courage) and Temperantia (moderation) are also favourite figures of the panels and rolls (Fig. 40) on Renaissance bindings of the German type. The counterpart of Justitia is Fortuna, sometimes Lucretia or Judith. The thematic symmetry of the panels on the upper and lower cover exists here, too. A classical element was revived with the Janus-faced Prudence on a leather binding (Fig. 38). The inscription of the panel: "Seek advice from m e - - I who am called Prudentia--if you wish for counsel in your affairs." Janus, the Roman god with two opposite faces looking forward and backward, gives good advice and is considerate and provident like Prudentia on our panel. Janus is the god of all beginnings, and it is advisable to begin everything with consideration and circumspection, i.e. prudence. The virtues as well as the Muses (Fig. 40) and the seven liberal arts (Fig. 41) are as a rule represented in every field of Renaissance art, hence also in book illustrations (Fig. 42) and on bookbindings. Note the analogous depiction of arts and virtues in Fig. 41. If we see the panel of the Judgement of Solomon (1 Kings 3:16-28) on the upper cover then we see another scene from the Old Testament, viz. Samson with the lion a n d - - i n the background--he 866 M. ROZSONDAI and B. ROZSONDAI Fig. 38. G e r m a n Renaissance binding with a Reformer roll and a Prudentia panel. Bound by M W (meaning Melchior Wagner, Leipzig?) after 1567 [25]. Bibl. Acad. Budapest: RM IV 427. Symmetry aspects of bookbindings 867 Fig. 39. Justitia and Fortuna on the upper and lower cover, respectively, of a German Renaissance binding by H W (meaning Hans Welcker, Nuremberg?) [25]. Daniel Wintzenberger: Warhafftige Geschichte und gedenckwirdiger Hiindel... Dresden (1583). The inscription under Justitia: "Suum cuique juste tribuo" is a saying attributed to the Roman jurist Ulpianus; under the "ambiguous" Fortuna: a variant from Tristia 5.8.15 by Ovid. Bibl. Acad. Budapest: RM IV 428. is taking away the gates o f the city o f G a z a (Judges 14:6; 16:3) (Fig. 43). O r on a n o t h e r binding: T h e m o s t o u t s t a n d i n g he roine in the Old T e s t a m e n t is Judith (the b o o k n a m e d af ter her is one o f the A p o c r y p h a ) , w h o b e h e a d e d Hol ofe rne s, the general o f the Assyrian t r o o p s o f N e b u c h a d n e z z a r , and thus saved Israel f r o m its enemies. Judi th inspired m a n y artists to depict her and her feat in paintings, in sculptures a n d in metal engravings. In topical s y m m e t r y parallel to Judith, we see either Justitia holding a sword a n d a pa ir o f scales o r - - m o r e o f t e n - - J a e l , w h o inflicted something very similar o n a n o t h e r enemy, Sisera (Judges 4:21) (Fig. 44). T h e strongest t e s t i m o n y o f faith is A b r a h a m ' s readiness to offer his only son Isaac (Genesis 22). " N o one is so great as A b r a h a m ! W h o is capable o f u n d e r s t a n d i n g h i m ? " - - a s k s S~ren K i e r k e g a a r d (1813-1855), whose influence is larger t o d a y t h a n it was in his own time, a n d f or w h o m the story o f A b r a h a m was the greatest p a r a d o x o f faith. A n d yet he included a " P a n e g y r i c u p o n A b r a h a m " , " t h e knight o f f a i th", in his b o o k [26]. T h e example o f A b r a h a m ' s faith also fascinated customers w h o had their b o o k s b o u n d in the sixteenth century. On a panel decor ating the u p p e r c o v e r o f a b o o k (Fig. 45) we see A b r a h a m with a sword in one hand, the o t h e r h a n d lying o n the head o f his son, w h o is bending f o r w a r d , a nd below, to the right, is the sacrificial fire in a pot, while in the centre o f the picture, in the b a c k g r o u n d , A b r a h a m is climbing M o u n t M o r i a h with Isaac and, finally, in the u p p e r right corner, is the angel o f the L o r d in the clouds, seizing A b r a h a m ' s sword. T h e inscription reads " A b r a h a m credidit d e o " - - A b r a h a m has believed in G o d . (Present perfect, as it has already been d e m o n s t r a t e d ! ) T h e middle panel o f the lower cover is d e c o r a t e d with the arms o f the D u k e s o f W i i r t t e m b e r g with the initials o f their m o t t o (Fig. 45): V D M I E - - V e r b u m D o m i n i m a n e t in [a]eternum (a va ri a nt o f Psalm 118 = 119: 89). T h e w o r d o f the L o r d remains f o r ever. We think that the panel o f A b r a h a m ' s sacrifice was chosen deliberately to emphasize the m o t t o and the arms, and this is again a case o f c o n c e p t u a l symmetry. Let us r e t u r n to K i e r k e g a a r d ' s vision a nd interpretation. H e sketches f o u r variants o f w h a t had h a p p e n e d and h o w the last act o f this sacrifice was reached [26]. Each o f them is fearful and shocking but what is m o r e a ma z i ng is t h a t he draws a parallel between the deed o f A b r a h a m and the weaning o f a child f r o m its m o t h e r . K i e r k e g a a r d comes to optimistic conclusions only in the cases o f the m o t h e r and child. F a t h e r a nd son, m o t h e r a n d child are presented in analogous s i t u a t i o n s - - a s regards a kind o f s e p a r a t i o n - - a n d in f o u r aspects. Intellectual s y m m e t r y is mostly indirect, hidden symmetry, w h a t is more , the symbolism itself is inherently symmetrical. T h e a u t h o r ' s life reveals a (o) (b) t } i i Fig. 40. Roils with representations o f the virtues (a), and the Muses (b). Bibl. Acad. Budapest: RM IV 177a, RM III F 175b, 542.169, RM III 92. Symmetry aspects of bookbindings 869 Fig. 41. The seven arts and the virtues on panels. Inscriptions (above) Grammatica-Dialectica-Redorica [!]-Arithmetica -Musica (two figures~--1574 (digit 4 reversed!)--Geometria-Astronomia; (below) Justicia [!]-Prudencia [!]-Fortitudo-Temperanci [!]-Fides-Spes--Charitas-Paciencia [!] [25]. Bibl. Acad. Budapest: 542.495, Ant. 944. CAMWA 17/4-6~Z 870 M. ROZSONDAI and B. ROZSONDAI Fig. 42. The nine Muses on the title page of Strabon: En tibi Strabonis geographicorum commentarios a C. Heresbachio recognitos. Valentenus Curio, Basileae (1523). Fig. 43. The Judgement o f Solomon and Samson with the lion on a binding by Caspar Kraft [25]. Bibl. Acad. Budapest: 542.150. Fig. 44. Judith with Holofernes and Jael with Sisera on a binding. Inscription under Judith from Psalm 144 = 145: 19; under Jael: Judges 5: 31. Bibl. Acad. Budapest: 542.496. Fig. 45. A b r a h a m ' s sacrifice and the coat o f arms o f the Dukes of Wiirttemberg on a'binding. Kurtze auszlegung iiber... Euangelia... in Crobatischer Sprach... (Ed. Primus Truber). Tiibingen (1562). Bibl. Acad. Budapest: R/tth 1772. 872 M. ROT_.~ONDAI and B. ROZSO~DAI ) ! i i i ;} I t i t! : i 2 ' ! i . . . . . . . . :ii Fig. 46. Biblical scenes on German Renaissance rolls. Metropolitan Szab6 Ervin Library, Budapest: Bq 0941/69; Bibl. Acad. Budapest: RM IV F 596, R~th 1069-70. Reproduced by permission. ( o ) Symmetry aspects of bookbindings ( b ) . . . . . . . . 873 Fig. 47. (a) A Justification panel. Pietro Martire Vermigli, In Epistolam S. Pauli Apostoli ad Romanos Commentarii. Perna, Basileae (1568). Bibl. Acad. Budapest: 543.024. (b) The Justification represented on two panels. Jean Calvin: lnstitutio Christianae religionis. Rebulius, G-enevae (1561). Bibl. Acad. Budapest: 542.080. further dimension of the structure. The retold story of Abraham and the parallel cases of mother and child are reflections of Kierkegaard's emotional crisis after his engagement and tragic rupture with Regina, subtle allusions to the waves in his soul of hope and despair, faith and final resignation. The scene of Abraham's sacrifice is often engraved on rolls, too, together with other scenes from the Bible. in general, such a roll consists of four little pictures. The Crucifixion and the Resurrection are represented on all three rolls shown (Fig. 46). These two scenes occur on panels in another connection [27]. The four scenes on the panel in Fig. 47(a) are divided by the tree of life: to the left the Fall (Adam and Eve under the tree o f knowledge of good and evil), underneath Damnation and Moses with the tablets o f stone; this side o f the tree is dead. The fight-hand side of it is in leaf, since this half o f the panel comprises the Crucifixion and the Resurrection. The complex theme and the method o f representation come from the paintings of the Allegory of the Fall and the Redemption or Justification by Lucas Cranach Sr and his workshop [28, 29]. These paintings and other similar ones, e.g. that in the Budapest Museum of Fine Arts (Fig. 48) reflect the idea--the exegesis o f Justification--of the great Reformer Martin Luther and his circle. In the painting in Budapest we can observe Mount Sinai, where the Lord God gave Moses the two tablets of stone, the Fall, the serpent o f brass and Death. In the middle Adam or Everyman is sitting between a Prophet and John the Baptist, both of them pointing to the Crucifix. Mary is kneeling on the top of a mount--opposite Moses--accepting a small child gliding down on golden rays; on the two sides of the Crucifix we see the Holy Lamb and the Bethlehem scene with the Angels, the shepherds, and the Holy Family in the stable; and at last Christ triumphant over Death. All this can hardly be accommodated on one panel [cf. Fig. 47(a)]. The picture of Justification, divided symmetrically into two parts along the tree, occurs commonly on two panels [Fig. 47(b)] on the upper and lower cover of the given leather binding. Sin and Justification, Law and Redemption, Death and Resurrection; grave-stone, skeleton, objects, persons, gestures and ideas are positioned in a wonderful antisymmetry, in other words implying less geometrical rigour, in a counterpoint. Even iffigural representations appear on a Gothic or Renaissance binding, no definite connection to the contents of the book can be recognized. (See the captions to the figures named here.) The book of sermons by Pelbartus de Tbemeswar is decorated by the insignia of the Passion (Fig. 16). The covers of a New Testament which was interpreted by B6ze and printed in Geneva were never- theless embellished by the portraits of Luther and Melanchthon (Fig. 37). It is of course thus, since the book was bound in Wittenberg, the stronghold of the Lutheran Reformation. Similarly, the Lutheran dogma of Justification is represented on Calvin's work [Fig. 47(b)]. Justitia appears on a 874 M. ROZSONDAI and B. ROT.~NDAI Fig. 48. Fall and Redemption (Law and Grace). Painting, German master, middle of the sixteenth century [30]. 82 x 59.5 cm. Deposited at the Budapest Museum of Fine Arts. Reproduced by permission. book of historical events (Fig. 39), and Abraham's sacrifice on a collection of Gospel commentaries (Fig. 45). FROM BAROQUE TO MODERN B I N D I N G S Baroque leather bindings catch the eye by their rich gold tooling (Fig. 49). Their characteristic ornamental elements are the elongated leafy spiral, the curl, borrowed from late Renaissance "fanfare" style bindings, voluted C- and S-shaped figures, sprays and floral motifs (Fig. 50). The asymmetrical spirals are skilfully combined to give heart-shaped and other symmetrical constructions, which in turn form the diamond or marquise-shaped central panel and the enchantingly harmonizing corner pieces. These masters must have had therefore a pair of stamps to impress both mirror image forms of the asymmetrical spiral motifs. Two or three borders run along the edges. One of these rolls (Fig. 50) reminds us of an arabesque circle border pattern used 200 years before [Fig. 27(b)]. The brightest period o f Hungarian Baroque bindings in the eighteenth century is associated with the Jesuits in Nagyszombat (today Trnava, Czechoslovakia), who maintained their Academy and Symmetry aspects of bookbindings 875 printing house there (predecessors o f E r t v r s University and the University Press, Budapest). These bindings bear Jesus' monogram, IHS, the Jesuits' sign in the middle o f the upper cover, and correspondingly the letters M A R I A on the lower cover (Fig. 50). There is no remarkable borderline between Baroque and rococo bindings. The frequent occurrence o f shellwork gave the name to the style (rocaille = shell, shellwork in French). The central piece is often omitted, and only the borders o f the cover(s) are decorated (Fig. 51). Books were the essential ornaments o f the splendid library halls o f the Baroque and later periods, and, very often, only the spines o f these books were embellished. A distinct period o f Hungarian binding began in the first half o f the eighteenth century and lasted for about a hundred years. The overwhelming majority o f these popular coloured parchment bindings was produced in the town o f wealthy urbanized peasants, Debrecen (Fig. 52). Their layout follows the interlace outlines o f French Renaissance bindings, and the uncoloured strips surround brightly coloured fields with guilt or coloured fleurons and the curls known from Baroque bindings. The master o f the binding in Fig. 52(a) even turns the flower-pot upside down for the sake o f preserving the symmetry o f the rectangle (C2v). Colouring seems to have been applied instinctively to enhance brilliance but no conscious colour symmetry appears. A curiosity o f b o o k construction, and an example o f a three-dimensional point-group symmetry is the dos-fi-dos binding (Fig. 53). Two, sometimes more books, related by their contents and usage, are bound together "back to back" with one common board and their spines on opposite sides. (a) Fig. 49--continued overleaf 876 M. ROZSONDAI and B. ROZSONDAI (b) Fig. 49. Hungarian Baroque bindings, eighlcenth century. (a) Bibl. Acad. Budapest: 542.987. (b) Metro- politan Szab6 Ervin Library, Budapest: Bf 0910/234 (MS). Reproduced by permission. Symmetry aspects of bookbindings 877 Fig. 50. Ornamental elements of Baroque bindings. The upper roll is from the binding in Fig. 49(a); the second roll is from the binding in Fig. 27(b). 878 M. ROZSONDAI and B. ROZSONDAI . . t 5 O e~ .=. O Symmetry aspects of bookbindings 879 ~ i i ~ i i ¸ ¸ ~ ! i i i i ! i i i i ! ! i ii~i!i~ !i~i ~i~i! i ~i!~ ~ ! ~ i ! ~ ~ ~ ~ ~ , ~ i i i i ~ ! i! ii~iii~iiiiiii~i~i~!ii!i~i~i~!ii!~ilziiiii~!~i ¸~¸ '̧̧ ¸~¸¸¸~ ~ ¸¸¸ ~ , ~ i ~ i i i ~ i i . . . . . . i ̧ ̧ ~ i i i i ~ i - i i o~ o o ° . .o . . L~ o~o t ~ 0 880 M. ROZ,gONDAI and B. ROZ,SONDAI Fig. 53. Hungarian dos-~t-dos binding, eighteenth century. E6tv6s Lorfind University Library, Budapest: RMK I 423a, RMK I 435 I-II. Reproduced by permission. (Another example and references can be found in Ref. [4, item 91].) This structure possesses a two-fold rotation axis parallel to the spines and a reflection plane perpendicular to it (point group C2h). HOW practical this form proves to be for a two-way pocket travel dictionary! In some m o d e m pocket dictionaries the two integrated parts have rather one common spine and no board in the middle between the "running" and the "reversed" pages. The symmetry o f this b o o k is again trivial, point group C2v, with the two-fold axis perpendicular to the spine. It is left to the reader to meditate on combinations o f symmetry operations with an inversion of, say, a Hungarian-Italian dictionary to its Italian-Hungarian counterpart. Some m o d e m artists have created three-dimensional bookbindings [31] that resemble rather a sculpture or space construction, and which have lost their practical purpose o f protecting and decorating a b o o k in use. Though masters o f Baroque and rococo bindings retained much o f the elements o f preceding late Renaissance (curls, arabesque circles, interlace outlines, layout) or even late Gothic bindings [bird- in-vine [32], and of. Fig. 18(b)], they succeeded in creating a new type o f bookbinding decoration, distinguished by its appearance and effect. The wells o f innovative power seem, however, to have been exhausted by the nineteenth century. At the same time when in architecture the different " n e o " styles follow, bookbinders cannot but historicize, and the period is marked by phrases like Etruscan style, Cathedral style, and flourishing species o f neo-Renaissance. It is in such nostalgic works that the technical perfection o f hand bookbinding reaches a level unknown before (Fig. 54). Para- Symmetry aspects of bookbindings 881 Fig. 54. Neo-Renaissance binding by Marius Michel for Gy6rgy Rfith, bibliophile, director of the Museum of Applied Arts, Budapest. End of the nineteenth century. Bibl. Acad. Budapest: R6.th 1044. Fig. 55. Art nouveau binding by Evelyn Underhill, fec. op. 47, 1902, England. Museum of Applied Arts, Budapest: Inv. 6965. Reproduced by permission. 882 M. RO7_.SONDAI and B. ROZSONDA1 Fig. 56. Representation o f the labyrinth on the external wall of the Cathedral in Lucca, Italy. Photograph by and courtesy of Istvfin Orosz, Budapest. Fig. 57. Binding by J. A. Szirmai, 1983-84. Terra-cotta goatskin (Niger), on front cover blind impression by the use o f a linocut. 32 x 25 cm. Cat. No. 45 [35]. Andr6 Gide: Theseus. Otilcina Bodoni, Verona (1949). Photograph by J. A. Szirmai. Reproduced by permission. Fig. 58. Binding by J. A. Szirmai, 1975-77. Dark grey goatskin (oasis), on front cover onlays in black and light grey goatskin. 29 x 20cm. Cat. No. 25 [35]. Julien Green: Adrienne Mesurat. Soci6t6 Les Exemplaires, Paris (1929). Photograph by 3. A. Szirmai. Reproduced by permission. Symmetry aspects of bookbindings 883 Fig. 59. Binding by J. A. Szirmai, 1972. Terra-cotta goatskin (oasis); onlays on front and back cover, partly crumpled, in yellow ochre, dark brown and green. 23.5 x 31.5 cm. Cat. No. 3 [35]. Hans Erni: Israel. Ein Skizzenbuch. Scheidegger, Zurich (1971). Photograph by J. A. Szirmai. Reproduced by permission. doxically, at the same time, b o o k b i n d i n g as a handicraft loses ground and declines with the advent o f machine binding. The turn o f the century is a l a n d m a r k in the art o f bookbinding. The m o d e r n b o o k b i n d e r claims to be an artist who creates a work o f art and n o t simply a decorated product o f handicraft; he or she re-creates the contents o f the book, expresses his or her impression o f the work to be bound. Principles a n d forms, artistic endeavour a n d materials o f m o d e r n fine art are reincarnated in m o d e r n bookbindings. A few examples have been selected here to show how apparently simple structures imply in the most intricate and sophisticated m a n n e r the arsenal o f " s y m m e t r o l o g y " [33]. Elements are consciously composed into a unit, and parts o f the book, upper and lower cover, are often treated as a whole (Fig. 55). The Labyrinth, originally the M i n o a n palace in Crete, has always provided an exciting adventure for the h u m a n mind, a source o f secret, a many-folded symbol, a m o n g others, o f the nether world and, at the same time, o f redemption from death [34]. W h a t it m e a n t for Comenius is concisely expressed in the title o f his work Labyrinth o f the Worm and the Paradise o f the Heart. It was represented in architecture (Fig. 56), arts and literature, as with, for example, the maze in the splendid book, Three Men in a Boat, by J. K. Jerome. Professor Szirmai's bookbinding (Fig. 57) is based on a circular symmetry, which is modified by a pseudo-symmetry o f four-fold rotation and reflection. Similarity is expressed by the set o f concentric circles, and c a t a m o r p h y , the lowest category o f geometrical relationships [33], by the decreasing number o f radial passages a n d dead ends along the inner circles. On a n o t h e r binding by Szirmai (Fig. 58), the double figure is again a brilliant and ingenious superposition o f two-fold rotational symmetry and deviation from it, symmetry and a n t i s y m m e t r y (two-colour symmetry o f the figure on a " n e u t r a l " background), and, above all, the transfiguration o f a p h e n o m e n o n taken from the contents o f the book. We must apologize to the reader for disclosing the keyword: it is schizophrenia. Figure 59 represents symmetry in a broad sense, so to say, a "topological s y m m e t r y " . Design and generalized symmetry extends over f r o n t a n d back cover. P. L. M a r t i n and M. Jeagle use rotations and reflections on their bindings .(Figs 60 and 61) combined with affine transformation, reflection with "blowing u p " (homothetic reflection [33]), and colour transformation. C O N C L U S I O N S T h r o u g h o u t the history o f b o o k b i n d i n g decoration, the rectangular form o f the book cover has been decisive. The general layout o f decorated leather bindings most often conforms to the two 884 M. ROZSONDAI and B. ROZSONDAI Fig. 60. Binding by Pierre Lucien Martin, 1966. Black box-calf, onlays in various shades of gray calf, doublures red peau de su6de. Ren6 Crevel: Feuilles eparses. Original illustrations by Bellmer, Arp, Miro, Ernst. Paris (1965). Fig. 61. Binding -by~Mart~i'n ' Jaegl"e_1973.' Dark biue-6asis goatskin, onlays in white, red and dark red, line tooling in white. Voltaire: Candide. m i r r o r p l a n e s o f t h e rectangle. O n e o r m o r e b o r d e r d e s i g n s a l o n g t h e sides leave a smaller, a g a i n r e c t a n g u l a r ( d e c o r a t e d ) a r e a in t h e m i d d l e . D e t a i l s o f R o m a n e s q u e a n d G o t h i c figures, a n i m a l s , floral m o t i f s , religious s y m b o l s , o r s u b d i v i s i o n o f fields d i s t u r b this s y m m e t r y . T h e o r i e n t a t i o n o f s u c h m o t i f s is i n f l u e n c e d b y the c o n v e n t i o n a l d i r e c t i o n o f view, i.e. the d i s t i n c t i o n b e t w e e n t o p a n d b o t t o m o f t h e b o o k c o v e r . T h e s y m m e t r i e s o f b o r d e r p a t t e r n s d o n o t i n d i c a t e a p r e f e r e n c e o f their o u t e r o r i n n e r edges. A unified g l o b a l c o m p o s i t i o n , the e m p h a s i s o n the c e n t r a l design, h a r m o n i z i n g b o r d e r d e c o r a t i o n a n d c e n t r e a n d c o r n e r pieces, a n d t h e s y m m e t r y o f details begin w i t h R e n a i s s a n c e b i n d i n g s , e i t h e r w i t h g e o m e t r i c o r floral p a t t e r n s o r w i t h p o r t r a i t s a n d scenes. I n t e r l a c e m o t i f s a n d p a t t e r n s b e c o m e a g a i n p o p u l a r . C o l o u r s y m m e t r y o c c u r s o n l y sparsely. B o o k b i n d i n g d e c o r a t i o n in e a c h age r e t a i n s s o m e e l e m e n t s f r o m its p r e v i o u s p e r i o d s a n d f o l l o w s w i t h a c e r t a i n d e l a y t h e m a i n styles o f t h e arts. D e c o r a t i o n r e q u i r e s i m a g i n a t i v e p o w e r a n d skill, a b o v e all in t h e case o f c u t l e a t h e r b i n d i n g s . S o m e nice parallels o f g e o m e t r y a n d s y m b o l s , d e p i c t e d scenes, p e r s o n s a n d ideas c a n be r e c o g n i z e d , nevertheless, t h e r e p r e s e n t a t i o n h a s h a r d l y a n y r e l a t i o n t o t h e c o n t e n t s o f the b o o k . T h e m o d e r n a r t o f b o o k b i n d i n g b r e a k s w i t h t r a d i t i o n . I t t r e a t s o n e o r b o t h b o o k c o v e r s a n d even the c o m p l e t e b o o k as a w h o l e . T h e n e c e s s i t y o f b o r d e r designs is e l i m i n a t e d . S y m m e t r y a n d the d i f f e r e n t k i n d s a n d levels o f g e o m e t r i c r e l a t i o n s a r e c o n s c i o u s l y a p p l i e d o r j u s t a b a n d o n e d . A n a l l u s i o n , a l b e i t indirect, t o t h e m e s s a g e in t h e b o o k is i n t e n d e d . Acknowledgements---Our thanks are due to Professor and Mrs Aladar and l~va Sarbu, Ms l~va Pr6hle and Mr Bob Dent, who read the manuscript and made valuable suggestions to amend its English. We gratefully acknowledge the permission and photographs for illustrations from institutions and persons named in the figure captions. R E F E R E N C E S 1. P. Gergely, P@ai Pgtriz-album a Magyar Tudomdnyos Akadbmia K6nyvtdrdban (The P~pai Pfiriz Album in the Library of the Hungarian Academy of Sciences). Publicationes Bibliothecae Academiae Scientiarum Hungaricae 21, Budapest (1961). 2. J. A. Comenius, Orbis Sensualium Pictus. Facsimile of the third London edn (1672) (Introduction J. Bowen). Sydney University Press, Sydney (1967). 3. F. Steenbock, Der kirchliche Prachteinband im friihen Mittelalter yon den Anfdngen bis zum Beginn der Gotik. Deutscher Verlag fiir Kunstwissenschaft, Berlin (1965). 4. P. Needham, Twelve Centuries o f Bookbindings 400-1600. The Pierpont Morgan Library--OUP, Oxford (1979). 5. F. A. Schmidt-Kfinsemfiller, Die abendla'ndischen romanischen Blindstempeleinbiinde. Hiersemann, Stuttgart (1985). 6. E. Panofsky, Gothic Architecture and Scholasticism. Archabbey Press, Latrobe, Pa. (1956). 7. G.D. Hobson, Further notes on Romanesque bindings. Library 15, 161-211 (1934-35); Some early bindings and binders' tools. Library 19, 202-249 (1938-39). 8. E. Kyriss, Verzierte Gotische Einbginde On alten deutschen Sprachgebiet. Textbandl Tafelband 1-3. 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Lengyel, The seven one-dimensional space-group symmetries illustrated by Hungarian folk needlework. J. Chem Educ. 61, 1033-1034 (1984). 16. M. Rozsondai, Historical fine bindings in the Library o f the Hungarian Academy of Sciences and their connection to book history (in Hungarian). Thesis, Budapest (1985). 17. D. Schattschneider, In black and white: how to create perfectly colored symmetric patterns. Comput. Math. Applic. 12B, 673-695 (1986). Reprinted in Symmetry: Unifying Human Understanding (Ed. I. Hargittai). Pergamon Press, Oxford (1986). 18. M. M. Foot-Romme, Influences from the Netherlands on bookbinding in England during the late fifteenth and early sixteenth centuries. Act. Xle Congr. Int. Bibl. pp. 39-64, Bruxelles (1979). 19. Cs. Csapodi, The Corvinian Library: History and Stock. Akad6miai Kiad6, Budapest (1973). 20. 1~. Sz. Koroknay, Oriental influences in Hungarian Renaissance bookbinding (in Hungarian). May. tb'rt. Ertesitb'(1-2), 1-17 (1968). 21. 1~. Sz. Koroknay, Eine ungarische Renaissance-Einbandgruppe vom Anfang des 16. Jahrhunderts. Gutenberg Jb 361-371 (1966). 22. 1. Schunke, Venezianische Renaissanceeinb/inde: Ihre Entwicklung undihre Werkst/itten. Studidibibliographiaedistoria in onore di Tammaro de Marinis. Vol. IV, pp. 123-200, Plate XXV, Verona (1964). 23. O. Mazal, Europfiische Einbandkunst aus Mittelalter und Neuzeit: 270 Einbiinde der Osterreichischen Nationalbibliothek. Plate 99. Akad. Druck- u. Verlagsanstalt, Graz (1970). 24. M. M. Foot, The Olga Hirsch collection of decorated papers. Br. Libr. J. 7 (1), 12-38 (1981). 25. M. Rozsondai, Signierte Renaissance-Einb/inde deutschen Typs aus dem 16. Jahrhundert. Gutenberg Jb 290--339 (1988). 26. S. Kierkegaard, Fear and Trembling... (Translated, introduction and notes by W. Lowrie). Princeton Univ. Press, Princeton, N.J. (1968). 27. K. von Rabenau, Reformation und Humanismus im Spiegel der Wittenberger Bucheinb/inde des 16. Jahrhunderts. Von der Macht der Bilder. Beitrage des C.I.H.A.-Kolloquiums "Kunst und Reformation" (Ed. E. Ullmann) pp. 319-328. Leipzig (1983). 28. Luc~is Cranach d.~., Verdammnis und Erl6sung (1529). Oltempera auf Lindenholz. 80 x 115 cm. Gotha, Museen der Stadt, Schlossmuseum. Inv. 722/676. 29. Lucas Cranach d..~. (Werkstatt), Siindenfall und Erldsung. (Um 1530). Nicht bez. Oltempera auf Holz. 51 x 99cm. Weimar, Kunstsammlungen, Galerie im Schloss. 30. Zs. Urbach, The allegory of the Fall and Redemption (in Hungarian). Diak6nia: Evangdlikus Szemle 5(2), 19-29 (1983). 31. Modern British Bookbinding. Bibliotheca Wittockiana, Bruxelles, Koninklijke Bibliotheek, 's Gravenhage 1985. Exhibition Catalogue. Designer Bookbinders, London (1985). 32. M. M. Foot, The Henry Davis Gift: A Collection o f Bookbindings. Vol. I, 2nd impression, Plate IV.19.A. The British Library, London (1982). 33. E. Makovicky, Symmetrology of art: coloured and generalized symmetries. Comput. Math. Applic. 12B, 949-980 (1986). Reprinted in Symmetry: Unifying Human Understanding (Ed. I. Hargittai). Pergamon Press, Oxford (1986). 34. K. Kerenyi, Labyrinth-Studien. Labyrinthos als Linienreflex einer mythologischen ldee. 2. erweiterte Aufl. Albae Vigiliae 10. Rhein, Ziirich (1950). 35. J. A. Szirmai, Boekbandkunst. Catalogus van boekbanden door J. A. S z i r m a i . . . i n de Universiteitsbibliotheek. Amsterdam (1984). CAMWA 17/4-~-AA