五维正六胞体

（6-超胞）
5-体

15 (3.3.3)
20 {3}
15

{3,3,3}x{}
{3,3}x{1}
{3,3}x{}x{}
{3}x{3}x{}
{3}x{}x{}x{}
{}x{}x{}x{}x{}

几何性质

坐标系

${\displaystyle \left({\sqrt {\frac {1}{15}}},\ {\sqrt {\frac {1}{10}}},\ {\sqrt {\frac {1}{6}}},\ {\sqrt {\frac {1}{3}}},\ \pm 1\right)}$
${\displaystyle \left({\sqrt {\frac {1}{15}}},\ {\sqrt {\frac {1}{10}}},\ {\sqrt {\frac {1}{6}}},\ -2{\sqrt {\frac {1}{3}}},\ 0\right)}$
${\displaystyle \left({\sqrt {\frac {1}{15}}},\ {\sqrt {\frac {1}{10}}},\ -{\sqrt {\frac {3}{2}}},\ 0,\ 0\right)}$
${\displaystyle \left({\sqrt {\frac {1}{15}}},\ -2{\sqrt {\frac {2}{5}}},\ 0,\ 0,\ 0\right)}$
${\displaystyle \left(-{\sqrt {\frac {5}{3}}},\ 0,\ 0,\ 0,\ 0\right)}$

图像

Ak

A5 A4

Ak

A3 A2

 正六超胞体的五维到四维施莱格尔图像（英语：Schlegel diagram）的四维到三维球极投影的三维到二维透视投影。

参考文献

• T. Gosset：On the Regular and Semi-Regular Figures in Space of n Dimensions，Messenger of Mathematics，Macmillan，1900
• H.S.M.考克斯特
• 考克斯特，Regular Polytopes，(第三版，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.考克斯特，Regular Polytopes，第三版，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
• (第22页) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
• (第23页) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
• (第24页) 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)
• 诺曼·约翰逊 Uniform Polytopes，Manuscript (1991)
• N.W.约翰逊: The Theory of Uniform Polytopes and Honeycombs，Ph.D. (1966)
• Richard Klitzing, 5D uniform polytopes (polytera), x3o3o3o3o - hix

{3,3,3,3} {4,3,3,3} {3,3,3,4}