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。

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）：

• 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.