Dodekeract

Dodekeract
Rank	12
Type	Regular
Space	Spherical
Notation
Coxeter diagram	x4o3o3o3o3o3o3o3o3o3o3o
Schläfli symbol	{4,3,3,3,3,3,3,3,3,3,3}
Elements
Henda	24 hendekeracts
Daka	264 dekeracts
Xenna	1760 enneracts
Yotta	7920 octeracts
Zetta	25344 hepteracts
Exa	59136 hexeracts
Peta	101376 penteracts
Tera	126720 tesseracts
Cells	112640 cubes
Faces	67584 squares
Edges	24576
Vertices	4096
Vertex figure	Dodecadakon, edge length √2
Measures (edge length 1)
Circumradius	$\sqrt3 ≈ 1.73205$
Inradius	$\frac12 = 0.5$
Hypervolume	1
Dixennal angle	90°
Height	1
Central density	1
Number of pieces	24
Level of complexity	1
Related polytopes
Army	*
Regiment	*
Dual	Tetrachiliaenneacontahexahendon
Conjugate	None
Abstract properties
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	B12, order 1961990553600
Convex	Yes
Nature	Tame

The dodekeract, also called the 12-cube or icositetrahendon, is one of the 3 regular polyhenda. It has 24 hendekeracts as facets, joining 3 to a xennon and 12 to a vertex.

It is the 12-dimensional hypercube. As such, it is a hexeract duoprism, tesseract trioprism, cube tetraprism and square hexaprism.

It can be alternated into a demidodekeract, which is uniform.

Vertex coordinates

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

• $\left(±\frac12,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac12\right).$