截角立方体堆砌

在几何学中,截角立方体堆砌是一种欧几里得三维空间的半正堆砌,由截角立方体正八面体堆砌而成,是三维空间内28个半正密铺之一,其对偶多面体为六双立方堆砌。

截角立方体堆砌
HC A2-P3.png
Truncated cubic tiling.png
线架图
类型均匀堆砌
维度3
对偶多胞形六双立方堆砌
类比截角正方形镶嵌
数学表示法
考克斯特符号
英语Coxeter-Dynkin diagram
node_1 4 node_1 3 node 4 node 
node_1 4 node_1 split1 nodes  = node_1 4 node_1 3 node 4 node_h0 
纤维流形记号4:2
施莱夫利符号t{4,3,4} or t0,1{4,3,4}
性质
3.8.8 Truncated hexahedron.png
{3,4} Uniform polyhedron-43-t2.svg
{3} Fire symbol (alchemical).svg
{8} Ośmiokąt foremny.PNG
组成与布局
顶点图Truncated cubic honeycomb verf.png
Isosceles 四角锥
对称性
对称群
空间群Pm3m (221)
考克斯特群, [4,3,4]
特性
顶点正英语vertex-transitive

康威截半立方体堆砌truncated cubille[1],因为它可以借由立方体堆砌经过“截角”变换构造而来。

表面涂色

Construction Bicantellated alternate cubic Truncated cubic honeycomb
考克斯特群 [4,31,1],   [4,3,4],  
=<[4,31,1]>
空间群 Fm3m Pm3m
表面涂色    
考克斯特符号英语Coxeter diagram       =                
顶点图    

参考文献

  • 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, 互联网档案馆
    • (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)