FIGURE ACKNOWLEDGEMENTS

THE PUBLISHERS EITHER have sought or are grateful to

the following for Permission to reproduce illustration material.

Figs4. 6 and 4.9 from D.A.Klarner（ed.），The mathe-matical Gardner（Wadsworth International，1981）.

Fig. 4.7from B.Grünbaumand G.C.She Phard, Tilings and Patterns（W.H.Freeman，1987）.Co Pyright?1987by W.H.Freeman and Com Pany.Usedby Permis-sion.

Fig. 4.10from K.Chand rasekharan, Hermann Weyl1885～1985（SPringer，1986）.

Figs. 4.11and10.3from Penta Plexity：a class of non-Period-ictilings of the Plane.The Mathematical Intelligencer，2，32～37（SPringer，1979）.

Fig. 4.12from H.S.M.Coxeter, M.Emmer, R.Pen-rose, and M.L.Teuber（eds），M.C.Escher：Artand science（North-Holland，1986）.

Fig. 5.2?1989 M.C.Escher Heirs/Cordon Art-Baarn-Holland.

Fig. 10.4from Journalof Materials Research，2，1～4（Materials Research Society，1987）.

All other figures（including4. 10and4.12）by the author. cVTgSPT41L8rAGXeqJHH+CA0yUosX+tntmV6h21J6OCv1cXsLUDX60sRpSCUrD5C