16-cube

16-cube
Rank	16
Type	Regular
Notation
Coxeter diagram	x4o3o3o3o3o3o3o3o3o3o3o3o3o3o3o ()
Schläfli symbol	{4,3,3,3,3,3,3,3,3,3,3,3,3,3,3}
Elements
Pedaka	32 pentadekeracts
Tedaka	480 tetradekeracts
Tradaka	4480 tridekeracts
Doka	29120 dodekeracts
Henda	139776 hendekeracts
Daka	512512 dekeracts
Xenna	1464320 enneracts
Yotta	3294720 octeracts
Zetta	5857280 hepteracts
Exa	8200192 hexeracts
Peta	8945664 penteracts
Tera	7454720 tesseracts
Cells	4587520 cubes
Faces	1966080 squares
Edges	524288
Vertices	65536
Vertex figure	15-simplex, edge length √2
Measures (edge length 1)
Circumradius	2
Inradius	${\frac {1}{2}}=0.5$
Hypervolume	1
Dixennal angle	90°
Height	1
Central density	1
Number of external pieces	32
Level of complexity	1
Related polytopes
Army	*
Regiment	*
Dual	16-orthoplex
Conjugate	None
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B16, order 1371195958099968000
Convex	Yes
Nature	Tame

The hexadekeract, also called the 16-cube or triacontadipedakon, is a regular 16-polytope. It has 32 pentadekeracts as facets, joining 3 to a peak and 16 to a vertex.

It is the 16-dimensional hypercube. As such it is an octeract duoprism, tesseract tetraprism, and square octaprism.

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

Vertex coordinates

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

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