Tetradekeract

Tetradekeract
Rank	14
Type	Regular
Notation
Coxeter diagram	x4o3o3o3o3o3o3o3o3o3o3o3o3o ()
Schläfli symbol	{4,3,3,3,3,3,3,3,3,3,3,3,3}
Elements
Tradaka	28 tridekeracts
Doka	364 dodekeracts
Henda	2912 hendekeracts
Daka	16016 dekeracts
Xenna	64064 enneracts
Yotta	192192 octeracts
Zetta	439296 hepteracts
Exa	768768 hexeracts
Peta	1025024 penteracts
Tera	1025024 tesseracts
Cells	745472 cubes
Faces	372736 squares
Edges	114688
Vertices	16384
Vertex figure	Tetradecadokon, edge length √2
Measures (edge length 1)
Circumradius	${\frac {\sqrt {14}}{2}}\approx 1.87083$
Inradius	${\frac {1}{2}}=0.5$
Hypervolume	1
Dixennal angle	90°
Height	1
Central density	1
Number of external pieces	28
Level of complexity	1
Related polytopes
Army	*
Regiment	*
Dual	Myriahexachiliatriacosioctacontatetratradakon
Conjugate	None
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B14, order 1428329123020800
Convex	Yes
Nature	Tame

The tetradekeract, also called the 14-cube or icosioctatradakon, is one of the 3 regular polytradaka. It has 28 tridekeracts as facets, joining 3 to a hendon and 14 to a vertex.

It is the 14-dimensional hypercube. As such it is a hepteract duoprism and square heptaprism.

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

Vertex coordinates

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

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