Pentadekeract

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Pentadekeract
15-cube.png
Rank15
TypeRegular
SpaceSpherical
Info
Coxeter diagramx4o3o3o3o3o3o3o3o3o3o3o3o3o3o
Schläfli symbol{4,3,3,3,3,3,3,3,3,3,3,3,3,3}
SymmetryB15, order 42849873690624000
Army*
Regiment*
Elements
Vertex figurePentadecatradakon, edge length 2
Tedaka30 tetradekeracts
Tradaka420 tridekeracts
Doka3640 dodekeracts
Henda21840 hendekeracts
Daka96096 dekeracts
Xenna320320 enneracts
Yotta823680 octeracts
Zetta1647360 hepteracts
Exa2562560 hexeracts
Peta3075072 penteracts
Tera2795520 tesseracts
Cells1863680 cubes
Faces860160 squares
Edges245760
Vertices32768
Measures (edge length 1)
Circumradius15/2 ≈ 1.93649
Inradius1/2 = 0.5
Hypervolume1
Dixennal angle90°
Central density1
Euler characteristic2
Related polytopes
DualTrismyriadischiliaheptacosihexacontoctatedakon
ConjugatePentadekeract
Properties
ConvexYes
OrientableYes
NatureTame

The pentadekeract, also called the 15-cube or triacontatedakon, is one of the 3 regular polytedaka. It has 30 tetradekeracts as facets, joining 3 to a dokon and 15 to a vertex.

It is the 15-dimensional hypercube. As such it is a penteract trioprism and cube pentaprism.

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

Vertex coordinates[edit | edit source]

The vertices of a pentadekeract 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).