Dekeract

Dekeract
(OFF file)
Rank	10
Type	Regular
Notation
Bowers style acronym	Deker
Coxeter diagram	x4o3o3o3o3o3o3o3o3o ()
Schläfli symbol	{4,3,3,3,3,3,3,3,3}
Tapertopic notation	1111111111
Toratopic notation	IIIIIIIIII
Bracket notation	[IIIIIIIIII]
Elements
Xenna	20 enneracts
Yotta	180 octeracts
Zetta	960 hepteracts
Exa	3360 hexeracts
Peta	8064 penteracts
Tera	13440 tesseracts
Cells	15360 cubes
Faces	11520 squares
Edges	5120
Vertices	1024
Vertex figure	Decayotton, edge length √2
Measures (edge length 1)
Circumradius	${\frac {\sqrt {10}}{2}}\approx 1.58114$
Inradius	${\frac {1}{2}}=0.5$
Hypervolume	1
Dixennal angle	90º
Height	1
Central density	1
Number of external pieces	20
Level of complexity	1
Related polytopes
Army	Deker
Regiment	Deker
Dual	Chiliaicositetraxennon
Conjugate	None
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B10, order 3715891200
Flag orbits	1
Convex	Yes
Net count	26941775019280
Nature	Tame

The 10-cube, also called the icosaxennon, dekeract, or deker, is one of the 3 regular 10-polytopes. It has 20 8-cubes as facets, joining 3 to a 7-cube peak and 10 to a vertex.

It is the 10-dimensional hypercube. It is also a 5-cube duoprism and a square pentaprism.

It can be alternated into a 10-demicube, which is uniform.

Vertex coordinates

The vertices of a 10-cube of edge length 1, centered at the origin, are given by:

• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right)$.

External links

• Klitzing, Richard. "deker".
• Wikipedia contributors. "10-cube".