Rank16
TypeRegular
SpaceSpherical
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
Measures (edge length 1)
Inradius$\frac12 = 0.5$ Hypervolume1
Dixennal angle90°
Height1
Central density1
Number of pieces32
Level of complexity1
Related polytopes
Army*
Regiment*
DualHexamyriapentachiliapentacositriacontahexapedakon
ConjugateNone
Abstract properties
Euler characteristic0
Topological properties
OrientableYes
Properties
SymmetryB16, order 1371195958099968000
ConvexYes
NatureTame

The hexadekeract, also called the 16-cube or triacontadipedakon, is one of the 3 regular polypedaka. It has 32 pentadekeracts as facets, joining 3 to a tradakon 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:

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