7-demicube

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7-demicube
Rank7
TypeUniform
Notation
Bowers style acronymHesa
Coxeter diagramx3o3o *b3o3o3o3o ()
Elements
Exa64 heptapeta, 14 demihexeracts
Peta448 hexatera, 84 demipenteracts
Tera1344 pentachora, 280 hexadecachora
Cells560+2240 tetrahedra
Faces2240 triangles
Edges672
Vertices64
Vertex figureRectified heptapeton, edge length 1
Measures (edge length 1)
Circumradius
Hypervolume
Diexal anglesHax–hix–hop:
 Hax–hin–hax: 90°
Height
Central density1
Number of external pieces78
Level of complexity5
Related polytopes
ArmyHesa
RegimentHesa
DualSemistellated hecatonicosoctaexon
ConjugateNone
Abstract & topological properties
Flag count1612800
Euler characteristic2
OrientableYes
Properties
SymmetryD7, order 322560
ConvexYes
NatureTame

The demihepteract, or hesa, also called the hemihepteract or 7-demicube, is a convex uniform polyexon. It has 14 demihexeracts and 64 heptapeta as facets, with 7 of each at a vertex forming a rectified heptapeton as the vertex figure. It is the 7-dimensional demihypercube and is formed by alternating the hepteract. It is also a segmentoexon, as a demihexeractic antiprism.

The demihepteract contains the vertices of a tetrahedral-hexadecachoric duoprism.

Vertex coordinates[edit | edit source]

The vertices of a demihepteract of edge length 1, centered at the origin, are given by all even sign changes of:

Representations[edit | edit source]

A demihepteract has the folowing Coxeter diagrams:

  • x3o3o *b3o3o3o3o (full symmetry)
  • s4o3o3o3o3o3o (as alternated hepteract)
  • xo3oo3ox *b3oo3oo3oo&#x (D6 axial, demihexeract antiprism)
  • oooo3oxoo3oooo3ooxo3oooo3ooox&#xt (A6 axial, vertex-first)
  • oxoo3ooxo xoxo3oooo3oxox *d3oooo&#xt (D4×A2 symmetry, hexadecachoron-first)
  • xo3oo3ox *b3oo xo3oo3ox&#zx (D4×A3 symmetry, hull of two tetrahedral-hexadecachoric duoprisms)

External links[edit | edit source]