Tridekeract

Tridekeract
Rank	13
Type	Regular
Notation
Coxeter diagram	x4o3o3o3o3o3o3o3o3o3o3o3o ()
Schläfli symbol	{4,3,3,3,3,3,3,3,3,3,3,3}
Elements
Doka	26 dodekeracts
Henda	312 hendekeracts
Daka	2288 dekeracts
Xenna	11440 enneracts
Yotta	41184 octeracts
Zetta	109824 hepteracts
Exa	219648 hexeracts
Peta	329472 penteracts
Tera	366080 tesseracts
Cells	292864 cubes
Faces	159744 squares
Edges	53248
Vertices	8192
Vertex figure	Tridecahendon, edge length √2
Measures (edge length 1)
Circumradius	${\frac {\sqrt {13}}{2}}\approx 1.80278$
Inradius	${\frac {1}{2}}=0.5$
Hypervolume	1
Dixennal angle	90°
Central density	1
Number of external pieces	26
Level of complexity	1
Related polytopes
Army	*
Regiment	*
Dual	Octachiliahecatonenneacontadidokon
Conjugate	None
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	B13, order 51011754393600
Convex	Yes
Nature	Tame

The tridekeract, also called the 13-cube or icosihexadokon, is one of the 3 regular polydoka. It has 26 dodekeracts as facets, joining 3 to a dakon and 13 to a vertex.

It is the 13-dimensional hypercube.

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

Vertex coordinates

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

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