截角五维超正方体

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截角五维超正方体
Type 五维均匀多胞体
施莱夫利符号 t{4,3,3,3}
考克斯特-迪金点图 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
四维胞 42
200
400
400
顶点 160
顶点图 Truncated 5-cube verf.png
Elongated tetrahedral pyramid
考克斯特点群 BC5, [3,3,3,4]
特性 convex

截角五维超正方体可以通过在每条棱距离顶点1/(\sqrt{2}+2)处截断五维超正方体的顶点来得到。每个被截断的顶点会产生一个新的正五胞体

坐标[编辑]

一个棱长为2的截角五维超正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}),\ \pm(1+\sqrt{2})\right)

投影[编辑]

正交投影
考克斯特平面 B5 B4 / D5 B3 / D4 / A2
Graph 5-cube t01.svg 5-cube t01 B4.svg 5-cube t01 B3.svg
二面体群 [10] [8] [6]
考克斯特平面 B2 A3
Graph 5-cube t01 B2.svg 5-cube t01 A3.svg
二面体群 [4] [4]

截角五维超正方体是各维度截角超方形中的第四个:

截角超方形
Regular polygon 8 annotated.svg 3-cube t01.svgTruncated hexahedron.png 4-cube t01.svgSchlegel half-solid truncated tesseract.png 5-cube t01.svg5-cube t01 A3.svg 6-cube t01.svg6-cube t01 A5.svg 7-cube t01.svg7-cube t01 A5.svg 8-cube t01.svg8-cube t01 A7.svg ...
八边形 截角立方体 截角正八胞体 截角五维超正方体 截角六维超正方体 截角七维超正方体 截角八维超正方体
CDel node 1.pngCDel 4.pngCDel node 1.png CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.png CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png

参考文献[编辑]

  • H.S.M. Coxeter:
    • H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
    • 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]
  • Norman Johnson Uniform Polytopes, Manuscript (1991)
    • N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D.
  • Richard Klitzing, 5D, uniform polytopes (polytera) o3o3o3x4x - tan, o3o3x3x4o - bittin

外部链接[编辑]