Demidekeract (10-demicube) | ||
---|---|---|
![]() Petrie polygon projection | ||
Type | Uniform 10-polytope | |
Family | demihypercube | |
Coxeter symbol | 171 | |
Schläfli symbol | {31,7,1} h{4,38} s{21,1,1,1,1,1,1,1,1} | |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9-faces | 532 | 20
{31,6,1}
![]() 512 {38} ![]() |
8-faces | 5300 | 180
{31,5,1}
![]() 5120 {37} ![]() |
7-faces | 24000 | 960
{31,4,1}
![]() 23040 {36} ![]() |
6-faces | 64800 | 3360
{31,3,1}
![]() 61440 {35} ![]() |
5-faces | 115584 | 8064
{31,2,1}
![]() 107520 {34} ![]() |
4-faces | 142464 | 13440
{31,1,1}
![]() 129024 {33} ![]() |
Cells | 122880 | 15360
{31,0,1}
![]() 107520 {3,3} ![]() |
Faces | 61440 |
{3}
![]() |
Edges | 11520 | |
Vertices | 512 | |
Vertex figure |
Rectified 9-simplex![]() | |
Symmetry group | D10, [37,1,1] = [1+,4,38 [29+ | |
Dual | ? | |
Properties | convex |
In geometry, a 10-demicube or demidekeract is a uniform 10-polytope, constructed from the 10-cube with alternated vertices removed. It is part of a dimensionally infinite family of uniform polytopes called demihypercubes.
E. L. Elte identified it in 1912 as a semiregular polytope, labeling it as HM10 for a ten-dimensional half measure polytope.
Coxeter named this polytope as 171 from its
Coxeter diagram, with a ring on one of the 1-length branches, and
Schläfli symbol or {3,37,1}.
Cartesian coordinates for the vertices of a demidekeract centered at the origin are alternate halves of the dekeract:
with an odd number of plus signs.
![]() B10 coxeter plane |
![]() D10 coxeter plane (Vertices are colored by multiplicity: red, orange, yellow, green = 1,2,4,8) |
A regular dodecahedron can be embedded as a regular skew polyhedron within the vertices in the 10-demicube, possessing the same symmetries as the 3-dimensional dodecahedron. [1]
Demidekeract (10-demicube) | ||
---|---|---|
![]() Petrie polygon projection | ||
Type | Uniform 10-polytope | |
Family | demihypercube | |
Coxeter symbol | 171 | |
Schläfli symbol | {31,7,1} h{4,38} s{21,1,1,1,1,1,1,1,1} | |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9-faces | 532 | 20
{31,6,1}
![]() 512 {38} ![]() |
8-faces | 5300 | 180
{31,5,1}
![]() 5120 {37} ![]() |
7-faces | 24000 | 960
{31,4,1}
![]() 23040 {36} ![]() |
6-faces | 64800 | 3360
{31,3,1}
![]() 61440 {35} ![]() |
5-faces | 115584 | 8064
{31,2,1}
![]() 107520 {34} ![]() |
4-faces | 142464 | 13440
{31,1,1}
![]() 129024 {33} ![]() |
Cells | 122880 | 15360
{31,0,1}
![]() 107520 {3,3} ![]() |
Faces | 61440 |
{3}
![]() |
Edges | 11520 | |
Vertices | 512 | |
Vertex figure |
Rectified 9-simplex![]() | |
Symmetry group | D10, [37,1,1] = [1+,4,38 [29+ | |
Dual | ? | |
Properties | convex |
In geometry, a 10-demicube or demidekeract is a uniform 10-polytope, constructed from the 10-cube with alternated vertices removed. It is part of a dimensionally infinite family of uniform polytopes called demihypercubes.
E. L. Elte identified it in 1912 as a semiregular polytope, labeling it as HM10 for a ten-dimensional half measure polytope.
Coxeter named this polytope as 171 from its
Coxeter diagram, with a ring on one of the 1-length branches, and
Schläfli symbol or {3,37,1}.
Cartesian coordinates for the vertices of a demidekeract centered at the origin are alternate halves of the dekeract:
with an odd number of plus signs.
![]() B10 coxeter plane |
![]() D10 coxeter plane (Vertices are colored by multiplicity: red, orange, yellow, green = 1,2,4,8) |
A regular dodecahedron can be embedded as a regular skew polyhedron within the vertices in the 10-demicube, possessing the same symmetries as the 3-dimensional dodecahedron. [1]