凸均匀堆砌

在几何学中，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。

已知存在28种有此性质的堆砌（蜂巢体）：

立方体堆砌及其七个变换；
四面体-八面体堆砌（英语：tetrahedral-octahedral honeycomb）及其四个变换；
十种柱体形式的平面半正镶嵌（若包含立方体堆砌则为11种）；
5种由上面的几何体通过延伸或回转变换之几何体。

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

外部链接

埃里克·韦斯坦因. Honeycomb. MathWorld.
Uniform Honeycombs in 3-Space （页面存档备份，存于互联网档案馆） VRML models
Elementary Honeycombs （页面存档备份，存于互联网档案馆） Vertex transitive space filling honeycombs with non-uniform cells.
Uniform partitions of 3-space, their relatives and embedding （页面存档备份，存于互联网档案馆）, 1999
The Uniform Polyhedra （页面存档备份，存于互联网档案馆）
Virtual Reality Polyhedra （页面存档备份，存于互联网档案馆） The Encyclopedia of Polyhedra
lu.de/ octet truss animation （页面存档备份，存于互联网档案馆）
Review: A. F. Wells, Three-dimensional nets and polyhedra, H. S. M. Coxeter (Source: Bull. Amer. Math. Soc. Volume 84, Number 3 (1978), 466-470.) （页面存档备份，存于互联网档案馆）
Klitzing, Richard. 3D Euclidean tesselations. bendwavy.org.