凸均勻堆砌

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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.

幾何學中,凸均勻堆砌,又稱三維凸均勻蜂巢體(英语Convex uniform honeycomb),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。

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[编辑]


  • 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[编辑]