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：），是一種三維正密鋪，指能夠填滿歐幾里得空間的凸均勻多面體組成的空間堆砌。
四面體—八面體堆砌是28種三維歐幾里得空間的均勻堆砌之一, composed of alternating yellow tetrahedra and red octahedra.
存在28種有此性質的堆砌（蜂巢體）
- 立方體堆砌和七種變換過的堆砌
- 四面體—八面體堆砌和四種變換過的堆砌
- 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種是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. . Dover Publications, Inc. 1979. ISBN 0-486-23729-X. (Chapter 5: Polyhedra packing and space filling)
- Critchlow, Keith. . 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
- (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
- 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. . California: University of California Press Berkeley. 1976. ISBN 0-520-03056-7. Chapter 5. Joining polyhedra
外部連結
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维基共享资源中相关的多媒体资源：凸均勻堆砌 |
- 埃里克·韦斯坦因. . MathWorld.
- Uniform Honeycombs in 3-Space VRML models
- Elementary Honeycombs Vertex transitive space filling honeycombs with non-uniform cells.
- Uniform partitions of 3-space, their relatives and embedding, 1999
- The Uniform Polyhedra
- Virtual Reality Polyhedra The Encyclopedia of Polyhedra
- octet truss animation
- 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.)
- Richard Klitzing, 3D, Euclidean tesselations
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