截角超立方體

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截角超立方体
Schlegel half-solid truncated tesseract.png
類型 均匀多胞体
24
8 3.8.8 Truncated hexahedron.png
16 3.3.3 Tetrahedron.png
88
64 {3}
24 {8}
128
頂點 64
顶点图 Truncated 8-cell verf.png
Isosceles triangular pyramid
施萊夫利符號 t0,1{4,3,3}
考克斯特圖 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
參考索引 12 13 14
考克斯特群 BC4, [4,3,3], order 384
特性 convex

截角超立方体有24个:8个截角立方体,和16个正四面体

坐标[编辑]

截角超立方体可以通过在每条棱距离顶点1/(\sqrt{2}+2)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:

\left(\pm1,\ \pm(1+\sqrt{2}),\ \pm(1+\sqrt{2}),\ \pm(1+\sqrt{2})\right)

投影[编辑]

正交投影
考克斯特平面 B4 B3 / D4 / A2 B2 / D3
Graph 4-cube t01.svg 4-cube t01 B3.svg 4-cube t01 B2.svg
二面体群 [8] [6] [4]
考克斯特平面 F4 A3
Graph 4-cube t01 F4.svg 4-cube t01 A3.svg
二面体群 [12/3] [4]
Truncated tesseract net.png
展开图
Truncated tesseract stereographic (tC).png
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]
      • (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.
  • Richard Klitzing, 4D, uniform polytopes (polychora) o3o3o4o - tat, o3x3x4o - tah, x3x3o4o - thex


外部链接[编辑]