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,由截角立方体和正八面体堆砌而成,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 | |
---|---|
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 | = |
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 | |
胞 | 3.8.8 {3,4} |
面 | {3} {8} |
组成与布局 | |
顶点图 | 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 | |
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 | = | |
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.
- ^ 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)