Compound of two hexagonal antiprisms

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Compound of two hexagonal antiprisms
Rank3
TypeUniform
Notation
Coxeter diagramß2ß12o
Elements
Components2 hexagonal antiprisms
Faces24 triangles, 4 hexagons as 2 stellated dodecagons
Edges24+24
Vertices24
Vertex figureIsosceles trapezoid, edge lengths 1, 1, 1, 3
Measures (edge length 1)
Circumradius
Volume
Dihedral angles3–3:
 6–3:
Height
Central density2
Related polytopes
ArmySemi-uniform Twip, edge lengths (base), (sides)
Regiment*
DualCompound of two hexagonal antitegums
ConjugateCompound of two hexagonal antiprisms
Abstract & topological properties
Flag count192
OrientableYes
Properties
SymmetryI2(12)×A1, order 48
ConvexNo
NatureTame

The stellated dodecagonal antiprism or compound of two hexagonal antiprisms is a prismatic uniform polyhedron compound. It consists of 2 stellated dodecagons and 24 triangles. Each vertex joins one stellated dodecagon and three triangles. As the name suggests, it is an antiprism based on a stellated dodecagon.

Its quotient prismatic equivalent is the digonal-hexagonal duoantiprism, which is four-dimensional.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a stellated dodecagonal 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 two hexagons. In these cases the compound has only hexagonal antiprismatic symmetry and the convex hull is a dihexagonal alterprism.