Demihepteract

From Polytope Wiki
(Redirected from 7-demicube)
Jump to navigation Jump to search
Demihepteract
7-demicube t0 D7.svg
Rank7
TypeUniform
SpaceSpherical
Bowers style acronymHesa
Info
Coxeter diagramCDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
SymmetryD7, order 322560
ArmyHesa
RegimentHesa
Elements
Vertex figureRectified heptapeton, edge length 1
Exa64 heptapeta, 14 demihexeracts
Peta448 hexatera, 84 demipenteracts
Tera1344 pentachora, 280 hexadecachora
Cells560+2240 tetrahedra
Faces2240 triangles
Edges672
Vertices64
Measures (edge length 1)
Circumradius14/4 ≈ 0.93541
Hypervolume3112/5040 ≈ 0.087266
Diexal anglesHax–hix–hop: acos(–7/7) ≈ 112.20765°
 Hax–hin–hax: 90°
Height2/2 ≈ 0.70711
Central density1
Euler characteristic2
Related polytopes
DualSemistellated hecatonicosoctaexon
ConjugateDemihepteract
Properties
ConvexYes
OrientableYes
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 segmentopeton, 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:

  • (2/4, 2/4, 2/4, 2/4, 2/4, 2/4, 2/4).

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]