Hexadekeract

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Hexadekeract
Rank16
TypeRegular
SpaceSpherical
Info
Coxeter diagramx4o3o3o3o3o3o3o3o3o3o3o3o3o3o3o
Schläfli symbol{4,3,3,3,3,3,3,3,3,3,3,3,3,3,3}
SymmetryB16, order 1371195958099968000
Army*
Regiment*
Elements
Vertex figureHexadecatedakon, edge length 2
Pedaka32 pentadekeracts
Tedaka480 tetradekeracts
Tradaka4480 tridekeracts
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)
Circumradius2
Inradius1/2 = 0.5
Hypervolume1
Dixennal angle90°
Central density1
Euler characteristic0
Related polytopes
DualHexamyriapentachiliapentacositriacontahexapedakon
ConjugateHexadekeract
Properties
ConvexYes
OrientableYes
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[edit | edit source]

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

  • (±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2).