# Hepteract

Hepteract Rank7
TypeRegular
SpaceSpherical
Notation
Bowers style acronymHept
Coxeter diagramx4o3o3o3o3o3o (             )
Schläfli symbol{4,3,3,3,3,3}
Tapertopic notation1111111
Toratopic notationIIIIIII
Bracket notation[IIIIIII]
Elements
Exa14 hexeracts
Peta84 penteracts
Tera280 tesseracts
Cells560 cubes
Faces672 squares
Edges448
Vertices128
Vertex figureHeptapeton, edge length 2
Measures (edge length 1)
Circumradius$\frac{\sqrt7}{2} ≈ 1.32288$ Inradius$\frac12 = 0.5$ Hypervolume1
Diexal angle90°
Height1
Central density1
Number of pieces14
Level of complexity1
Related polytopes
ArmyHept
RegimentHept
DualHecatonicosoctaexon
ConjugateNone
Abstract properties
Net count33064966
Euler characteristic2
Topological properties
OrientableYes
Properties
SymmetryB7, order 645120
ConvexYes
NatureTame

The hepteract, or hept, also called the 7-cube, or tetradecaexon, is one of the 3 regular polyexa. It has 14 hexeracts as facets, joining 7 to a vertex. It is the 7-dimensional hypercube.

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

A regular octaexon of edge length 2 can be inscribed in the unit hepteract. The next largest simplex that can be inscribed in a hypercube is the dodecadakon.

## Vertex coordinates

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

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

A hepteract has the following Coxeter diagrams:

• x4o3o3o3o3o3o (full symmetry)
• x x4o3o3o3o3o (BC6×A1 symmetry, hexxeractic prism)
• x4o x4o3o3o3o (BC5×BC2 symmetry, square-penteractic duoprism)
• x4o3o x4o3o3o (BC4×BC3 symmetry, cubic-tesseractic duoprism)
• xx4oo3oo3oo3oo3oo&#x (BC6 axial)
• oqoooooo3ooqooooo3oooqoooo3ooooqooo3oooooqoo3ooooooqo&#xt (A6 axial, vertex-first)