凸均勻堆砌

在幾何學中，凸均勻堆砌，又稱三維凸均勻蜂巢體（英語：Convex uniform honeycomb），是一種三維正密鋪，由凸均勻多面體組成且能夠填滿歐幾里得空間。

已知存在28種有此性質的堆砌（蜂巢體）：

立方體堆砌及其七個變換；
四面體-八面體堆砌（英語：tetrahedral-octahedral honeycomb）及其四個變換；
十種柱體形式的平面半正鑲嵌（若包含立方體堆砌則為11種）；
5種由上面的幾何體通過延伸或迴轉變換之幾何體。

它們可以被認為是平面鑲嵌在三維空間的類比。

參考文獻

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

外部連結

埃里克·韋斯坦因. Honeycomb. MathWorld.
Uniform Honeycombs in 3-Space （頁面存檔備份，存於互聯網檔案館） VRML models
Elementary Honeycombs （頁面存檔備份，存於互聯網檔案館） Vertex transitive space filling honeycombs with non-uniform cells.
Uniform partitions of 3-space, their relatives and embedding （頁面存檔備份，存於互聯網檔案館）, 1999
The Uniform Polyhedra （頁面存檔備份，存於互聯網檔案館）
Virtual Reality Polyhedra （頁面存檔備份，存於互聯網檔案館） The Encyclopedia of Polyhedra
lu.de/ octet truss animation （頁面存檔備份，存於互聯網檔案館）
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.) （頁面存檔備份，存於互聯網檔案館）
Klitzing, Richard. 3D Euclidean tesselations. bendwavy.org.