Pentic 7-cubes
7-demicube (half 7-cube, h{4,35 })
Pentic 7-cube h5 {4,35 }
Penticantic 7-cube h2,5 {4,35 }
Pentiruncic 7-cube h3,5 {4,35 }
Pentiruncicantic 7-cube h2,3,5 {4,35 }
Pentisteric 7-cube h4,5 {4,35 }
Pentistericantic 7-cube h2,4,5 {4,35 }
Pentisteriruncic 7-cube h3,4,5 {4,35 }
Penticsteriruncicantic 7-cube h2,3,4,5 {4,35 }
Orthogonal projections in D7 Coxeter plane
In seven-dimensional geometry , a pentic 7-cube is a convex uniform 7-polytope , related to the uniform 7-demicube . There are 8 unique forms.
Pentic 7-cube
Cartesian coordinates
The Cartesian coordinates for the vertices of a pentic 7-cube centered at the origin are coordinate permutations:
(±1,±1,±1,±1,±1,±3,±3)
with an odd number of plus signs.
Images
Related polytopes
Dimensional family of pentic n-cubes
n
6
7
8
[1+ ,4,3n-2 ] = [3,3n-3,1 ]
[1+ ,4,34 ] = [3,33,1 ]
[1+ ,4,35 ] = [3,34,1 ]
[1+ ,4,36 ] = [3,35,1 ]
Cantic figure
Coxeter
=
=
=
Schläfli
h5 {4,34 }
h5 {4,35 }
h5 {4,36 }
Penticantic 7-cube
Images
Pentiruncic 7-cube
Images
Pentiruncicantic 7-cube
Images
Pentisteric 7-cube
Images
Pentistericantic 7-cube
Images
Pentisteriruncic 7-cube
Images
Pentisteriruncicantic 7-cube
Images
Related polytopes
This polytope is based on the 7-demicube , a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.
There are 95 uniform polytopes with D7 symmetry, 63 are shared by the BC7 symmetry, and 32 are unique:
D7 polytopes
t0 (141 )
t0,1 (141 )
t0,2 (141 )
t0,3 (141 )
t0,4 (141 )
t0,5 (141 )
t0,1,2 (141 )
t0,1,3 (141 )
t0,1,4 (141 )
t0,1,5 (141 )
t0,2,3 (141 )
t0,2,4 (141 )
t0,2,5 (141 )
t0,3,4 (141 )
t0,3,5 (141 )
t0,4,5 (141 )
t0,1,2,3 (141 )
t0,1,2,4 (141 )
t0,1,2,5 (141 )
t0,1,3,4 (141 )
t0,1,3,5 (141 )
t0,1,4,5 (141 )
t0,2,3,4 (141 )
t0,2,3,5 (141 )
t0,2,4,5 (141 )
t0,3,4,5 (141 )
t0,1,2,3,4 (141 )
t0,1,2,3,5 (141 )
t0,1,2,4,5 (141 )
t0,1,3,4,5 (141 )
t0,2,3,4,5 (141 )
t0,1,2,3,4,5 (141 )
Notes
References
H.S.M. Coxeter :
H.S.M. Coxeter, Regular Polytopes , 3rd Edition, Dover New York, 1973
Kaleidoscopes: Selected Writings of H.S.M. Coxeter , edited 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.
Klitzing, Richard. "7D uniform polytopes (polyexa)" .
External links