凸均匀堆砌

几何学中,凸均匀堆砌,又称三维凸均匀蜂巢体(英语:Convex uniform honeycomb),是一种三维正密铺,由凸均匀多面体组成且能够填满欧几里得空间。

四面体-八面体堆砌是28种三维欧几里得空间的均匀堆砌之一,由黄色的四面体和红色的八面体相间构成。

已知存在28种有此性质的堆砌(蜂巢体):

它们可以被认为是平面镶嵌在三维空间的类比。

参考文献

  • John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, (2008) The Symmetries of Things, ISBN 978-1-56881-220-5 (Chapter 21, Naming the Archimedean and Catalan polyhedra and tilings, Architectonic and Catoptric tessellations, p 292-298, includes all the nonprismatic forms)
  • George Olshevsky, (2006, Uniform Panoploid Tetracombs, Manuscript (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
  • Branko Grünbaum, (1994) Uniform tilings of 3-space. Geombinatorics 4, 49 - 56.
  • Norman Johnson (1991) Uniform Polytopes, Manuscript
  • Williams, Robert. The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. 1979. ISBN 0-486-23729-X.  (Chapter 5: Polyhedra packing and space filling)
  • Critchlow, Keith. Order in Space: A design source book. Viking Press. 1970. ISBN 0-500-34033-1. 
  • Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [1]
    • (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10] (1.9 Uniform space-fillings)
  • A. Andreini, (1905) Sulle reti di poliedri regolari e semiregolari e sulle corrispondenti reti correlative (On the regular and semiregular nets of polyhedra and on the corresponding correlative nets), Mem. Società Italiana della Scienze, Ser.3, 14 75–129. PDF [2]
  • D. M. Y. Sommerville, (1930) An Introduction to the Geometry of n Dimensions. New York, E. P. Dutton, . 196 pp. (Dover Publications edition, 1958) Chapter X: The Regular Polytopes
  • Anthony Pugh. Polyhedra: A visual approach. California: University of California Press Berkeley. 1976. ISBN 0-520-03056-7.  Chapter 5. Joining polyhedra

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