Demidekeract (10-demicube) | ||
---|---|---|
Petrie polygon projection | ||
Type | Uniform 10-polytope | |
Family | demihypercube | |
Coxeter symbol | 1_{71} | |
Schläfli symbol | {3^{1,7,1}} h{4,3^{8}} s{2^{1,1,1,1,1,1,1,1,1}} | |
Coxeter diagram | = | |
9-faces | 532 | 20 {3^{1,6,1}} 512 {3^{8}} |
8-faces | 5300 | 180 {3^{1,5,1}} 5120 {3^{7}} |
7-faces | 24000 | 960 {3^{1,4,1}} 23040 {3^{6}} |
6-faces | 64800 | 3360 {3^{1,3,1}} 61440 {3^{5}} |
5-faces | 115584 | 8064 {3^{1,2,1}} 107520 {3^{4}} |
4-faces | 142464 | 13440 {3^{1,1,1}} 129024 {3^{3}} |
Cells | 122880 | 15360 {3^{1,0,1}} 107520 {3,3} |
Faces | 61440 | {3} |
Edges | 11520 | |
Vertices | 512 | |
Vertex figure | Rectified 9-simplex | |
Symmetry group | D_{10}, [3^{7,1,1}] = [1^{+},4,3^{8}] [2^{9}]^{+} | |
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 HM_{10} for a ten-dimensional half measure polytope.
Coxeter named this polytope as 1_{71} from its Coxeter diagram, with a ring on one of the 1-length branches, and Schläfli symbol or {3,3^{7,1}}.
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.
B_{10} coxeter plane |
D_{10} 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]}