# 16-cube

16-cube
Rank16
TypeRegular
Notation
Coxeter diagramx4o3o3o3o3o3o3o3o3o3o3o3o3o3o3o ()
Schläfli symbol{4,3,3,3,3,3,3,3,3,3,3,3,3,3,3}
Elements
Doka29120 dodekeracts
Henda139776 hendekeracts
Daka512512 dekeracts
Xenna1464320 enneracts
Yotta3294720 octeracts
Zetta5857280 hepteracts
Exa8200192 hexeracts
Peta8945664 penteracts
Tera7454720 tesseracts
Cells4587520 cubes
Faces1966080 squares
Edges524288
Vertices65536
Vertex figure15-simplex, edge length 2
Measures (edge length 1)
Inradius${\displaystyle {\frac {1}{2}}=0.5}$
Hypervolume1
Dixennal angle90°
Height1
Central density1
Number of external pieces32
Level of complexity1
Related polytopes
Army*
Regiment*
Dual16-orthoplex
ConjugateNone
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryB16, order 1371195958099968000
ConvexYes
NatureTame

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:

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