Compound of four octahedra (prismatic symmetry)

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Compound of four octahedra (prismatic symmetry)
Rank3
TypeUniform
Elements
Components4 octahedra
Faces24 triangles, 8 triangles as 2 tetratriangles
Edges24+24
Vertices24
Vertex figureSquare, edge length 1
Measures (edge length 1)
Circumradius
Volume
Dihedral angle
Height
Central density4
Related polytopes
ArmySemi-uniform Twip, edge lengths (base), (sides)
Regiment*
DualCompound of four cubes
ConjugateCompound of four octahedra
Abstract & topological properties
Flag count192
OrientableYes
Properties
SymmetryI2(12)×A1, order 48
ConvexNo
NatureTame

The tetratriangular antiprism or compound of four octahedra with prismatic symmetry is a prismatic uniform polyhedron compound. It consists of 2 tetratriangles and 24 triangles. Each vertex joins one tetratriangle and three triangles. As the name suggests, it is an antiprism based on a tetratriangle.

Its quotient prismatic equivalent is the triangular tetrahedroorthowedge alterprism, which is six-dimensional.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a tetratriangular antiprism of edge length 1 centered at the origin are given by:

Variations[edit | edit source]

This compound has variants where the bases are non-regular compounds of four triangles (seen as two-hexagram compounds). In these cases the compound has only hexagonal prismatic symmetry and the convex hull is a dihexagonal prism.