10-cube

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10-cube Dekeract
Orthogonal projection inside Petrie polygon Orange vertices are doubled, and central yellow one has four
Type	Regular 10-polytope e
Family	hypercube
Schläfli symbol	{4,38}
Coxeter-Dynkin diagram
9-faces	20 {4,37}
8-faces	180 {4,36}
7-faces	960 {4,35}
6-faces	3360 {4,34}
5-faces	8064 {4,33}
4-faces	13440 {4,3,3}
Cells	15360 {4,3}
Faces	11520 squares
Edges	5120 segments
Vertices	1024 points
Vertex figure	9-simplex
Petrie polygon	icosagon
Coxeter group	C10, [38,4]
Dual	10-orthoplex
Properties	convex, Hanner polytope

In geometry, a 10-cube is a ten-dimensional hypercube. It has 1024 vertices, 5120 edges, 11520 square faces, 15360 cubic cells, 13440 tesseract 4-faces, 8064 5-cube 5-faces, 3360 6-cube 6-faces, 960 7-cube 7-faces, 180 8-cube 8-faces, and 20 9-cube 9-faces.

It can be named by its Schläfli symbol {4,3⁸}, being composed of 3 9-cubes around each 8-face. It is sometimes called a dekeract, a portmanteau of tesseract (the 4-cube) and deka- for ten (dimensions) in Greek, It can also be called an icosaronnon or icosa-10-tope as a 10 dimensional polytope, constructed from 20 regular facets.

It is a part of an infinite family of polytopes, called hypercubes. The dual of a dekeract can be called a 10-orthoplex or decacross, and is a part of the infinite family of cross-polytopes.