Octahedron atop cube

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Octahedron atop cube
Rank4
TypeSegmentotope
Notation
Bowers style acronymOctacube
Coxeter diagramxo4oo3ox&#x
Elements
Cells8+12 tetrahedra, 6 square pyramids, 1 octahedron, 1 cube
Faces8+24+24 triangles, 6 squares
Edges12+12+24
Vertices6+8
Vertex figures6 square antiprisms, edge length 1
 8 triangular antipodiums, edge lengths 2 (large base) and 1 (small base and sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesTet–3–tet:
 Tet–3–oct:
 Tet–3–squippy:
 Cube–4–squippy:
Height
Central density1
Related polytopes
ArmyOctacube
RegimentOctacube
DualCubic-octahedral tegmoid
ConjugateOctahedron atop cube
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryB3×I, order 48
ConvexYes
NatureTame

The octahedron atop cube, or octacube, is a CRF segmentochoron (designated K-4.15 on Richard Klitzing's list). As the name suggests, it consists of a cube and an octahedron as bases, connected by 6 square pyramids and 8+12 tetrahedra.

It is also commonly referred to as a cubic or octahedral antiprism, as the two bases are a pair of dual polyhedra.

Vertex coordinates[edit | edit source]

The vertices of an octahedron atop cube segmentochoron of edge length 1 are given by:

  • and all permutations of its first 3 coordinates,

External links[edit | edit source]