截角立方體堆砌

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截角立方體堆砌
HC A2-P3.png
Truncated cubic tiling.png
線架圖
類型 均勻堆砌
維度 3
3.8.8 Truncated hexahedron.png
{3,4} Uniform polyhedron-43-t2.svg
{3} Alchemy fire symbol.svg
{8} Ośmiokąt foremny.PNG
顶点图 Truncated cubic honeycomb verf.png
Isosceles 四角錐
施萊夫利符號 t{4,3,4} or t0,1{4,3,4}
考克斯特記號英语Coxeter–Dynkin_diagram CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
CDel node 1.pngCDel 4.pngCDel node 1.pngCDel split1.pngCDel nodes.png = CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node h0.png
類比 截角正方形鑲嵌
對稱群
空間群 Pm3m (221)
考克斯特群 , [4,3,4]
纖維流形 4:2
對偶多胞體 六雙立方堆砌
特性 顶点正英语vertex-transitive

在幾何學中,截角立方體堆砌是一種歐幾里得三維空間的半正堆砌,由截角立方體正八面體堆砌而成,是三維空間內28個半正密鋪之一,其對偶多面體為六雙立方堆砌。

康威截半立方體堆砌truncated cubille[1],因為它可以藉由立方體堆砌經過「截角」變換構造而來。

表面塗色[编辑]

Construction Bicantellated alternate cubic Truncated cubic honeycomb
考克斯特群 [4,31,1], [4,3,4],
=<[4,31,1]>
空間群 Fm3m Pm3m
表面塗色 Truncated cubic honeycomb2.png Truncated cubic honeycomb.png
考克斯特符號英语Coxeter diagram CDel node 1.pngCDel 4.pngCDel node 1.pngCDel split1.pngCDel nodes.png = CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node h0.png CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
頂點圖 Bicantellated alternate cubic honeycomb verf.png Truncated cubic honeycomb verf.png

参考文獻[编辑]

  • George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (包含11个凸半正镶嵌、28个凸半正堆砌、和143个凸半正四维砌的全表)
  • Kaleidoscopes: Selected Writings of H.S.M. Coxeter, F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication参与编辑, 1995, ISBN 978-0-471-01003-6 [1]
    • (22页) H.S.M.考克斯特, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10] (1.9 半正空间镶嵌)
  • A. Andreini, 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 (1905) 75–129.
  1. ^ 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)