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截角超立方體

截角超立方体有24个:8个截角立方体,和16个正四面体

截角超立方体
施莱格尔投影
(可以看见正四面体胞)
類型均匀多胞体
識別
名稱截角超立方体
參考索引12 13 14
數學表示法
考克斯特符號
英语Coxeter-Dynkin diagram
施萊夫利符號t0,1{4,3,3}
性質
24
8 3.8.8
16 3.3.3
88
64 {3}
24 {8}
128
頂點64
組成與佈局
顶点图
Isosceles triangular pyramid
對稱性
考克斯特群BC4, [4,3,3], order 384
特性
convex

坐标 编辑

截角超立方体可以通过在每条棱距离顶点 处截断超立方体的每一个角来得到。每个截断的角会产生一个正四面体

一个棱长为2的截角超立方体的每个顶点的笛卡儿坐标系坐标为:

 

投影 编辑

正交投影
考克斯特平面 B4 B3 / D4 / A2 B2 / D3
Graph      
二面体群 [8] [6] [4]
考克斯特平面 F4 A3
Graph    
二面体群 [12/3] [4]
 
展开图
 
三维正交投影

参考文献 编辑

  • T. Gosset: On the Regular and Semi-Regular Figures in Space of n Dimensions, Messenger of Mathematics, Macmillan, 1900
  • H.S.M. Coxeter:
    • Coxeter, Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8, p. 296, Table I (iii): Regular Polytopes, three regular polytopes in n-dimensions (n≥5)
    • H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973, p. 296, Table I (iii): Regular Polytopes, three regular polytopes in n-dimensions (n≥5)
    • Kaleidoscopes: Selected Writings of H.S.M. Coxeter, editied by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [1] (页面存档备份,存于互联网档案馆
      • (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
      • (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
      • (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
  • John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 26. pp. 409: Hemicubes: 1n1)
  • Norman Johnson Uniform Polytopes, Manuscript (1991)
    • N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. (1966)
  • 2. Convex uniform polychora based on the tesseract (8-cell) and hexadecachoron (16-cell) - Models 13, 16, 17, George Olshevsky.
  • Klitzing, Richard. 4D uniform polytopes (polychora). bendwavy.org.  o3o3o4o - tat, o3x3x4o - tah, x3x3o4o - thex


外部链接 编辑

  • Paper model of truncated tesseract (页面存档备份,存于互联网档案馆) created using nets generated by Stella4D software

截角超立方體, 截角超立方体有24个胞, 8个截角立方体, 和16个正四面体, 截角超立方体施莱格尔投影, 可以看见正四面体胞, 類型均匀多胞体識別名稱截角超立方体參考索引12, 14數學表示法考克斯特符號, 英语, coxeter, dynkin, diagram, 施萊夫利符號t0, 性質胞248, 3面8864, 邊128頂點64組成與佈局顶点图isosceles, triangular, pyramid對稱性考克斯特群bc4, order, 384特性convex查论编, 目录, 坐标, 投影, 参考文献,. 截角超立方体有24个胞 8个截角立方体 和16个正四面体 截角超立方体施莱格尔投影 可以看见正四面体胞 類型均匀多胞体識別名稱截角超立方体參考索引12 13 14數學表示法考克斯特符號 英语 Coxeter Dynkin diagram 施萊夫利符號t0 1 4 3 3 性質胞248 3 8 8 16 3 3 3面8864 3 24 8 邊128頂點64組成與佈局顶点图Isosceles triangular pyramid對稱性考克斯特群BC4 4 3 3 order 384特性convex查论编 目录 1 坐标 2 投影 3 参考文献 4 外部链接坐标 编辑截角超立方体可以通过在每条棱距离顶点1 2 2 displaystyle 1 sqrt 2 2 nbsp 处截断超立方体的每一个角来得到 每个截断的角会产生一个正四面体 一个棱长为2的截角超立方体的每个顶点的笛卡儿坐标系坐标为 1 1 2 1 2 1 2 displaystyle left pm 1 pm 1 sqrt 2 pm 1 sqrt 2 pm 1 sqrt 2 right nbsp 投影 编辑正交投影 考克斯特平面 B4 B3 D4 A2 B2 D3Graph nbsp nbsp nbsp 二面体群 8 6 4 考克斯特平面 F4 A3Graph nbsp nbsp 二面体群 12 3 4 nbsp 展开图 nbsp 三维正交投影参考文献 编辑T Gosset On the Regular and Semi Regular Figures in Space of n Dimensions Messenger of Mathematics Macmillan 1900 H S M Coxeter Coxeter Regular Polytopes 3rd edition 1973 Dover edition ISBN 0 486 61480 8 p 296 Table I iii Regular Polytopes three regular polytopes in n dimensions n 5 H S M Coxeter Regular Polytopes 3rd Edition Dover New York 1973 p 296 Table I iii Regular Polytopes three regular polytopes in n dimensions n 5 Kaleidoscopes Selected Writings of H S M Coxeter editied by F Arthur Sherk Peter McMullen Anthony C Thompson Asia Ivic Weiss Wiley Interscience Publication 1995 ISBN 978 0 471 01003 6 1 页面存档备份 存于互联网档案馆 Paper 22 H S M Coxeter Regular and Semi Regular Polytopes I Math Zeit 46 1940 380 407 MR 2 10 Paper 23 H S M Coxeter Regular and Semi Regular Polytopes II Math Zeit 188 1985 559 591 Paper 24 H S M Coxeter Regular and Semi Regular Polytopes III Math Zeit 200 1988 3 45 John H Conway Heidi Burgiel Chaim Goodman Strass The Symmetries of Things 2008 ISBN 978 1 56881 220 5 Chapter 26 pp 409 Hemicubes 1n1 Norman Johnson Uniform Polytopes Manuscript 1991 N W Johnson The Theory of Uniform Polytopes and Honeycombs Ph D 1966 2 Convex uniform polychora based on the tesseract 8 cell and hexadecachoron 16 cell Models 13 16 17 George Olshevsky Klitzing Richard 4D uniform polytopes polychora bendwavy org o3o3o4o tat o3x3x4o tah x3x3o4o thex外部链接 编辑Paper model of truncated tesseract 页面存档备份 存于互联网档案馆 created using nets generated by Stella4D software 取自 https zh wikipedia org w index php title 截角超立方體 amp oldid 75256165, 维基百科,wiki,书籍,书籍,图书馆,

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