# Compound of two hexagonal antiprisms

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${\displaystyle {\frac {\sqrt {3+{\sqrt {3}}}}{2}}\approx 1.08766}$
Volume${\displaystyle 2{\sqrt {2+2{\sqrt {3}}}}\approx 4.67508}$
Dihedral angles3–3: ${\displaystyle \arccos \left({\frac {1-2{\sqrt {3}}}{3}}\right)\approx 145.22189^{\circ }}$
6–3: ${\displaystyle \arccos \left({\frac {3-2{\sqrt {3}}}{3}}\right)\approx 98.89943^{\circ }}$
Height${\displaystyle {\sqrt {{\sqrt {3}}-1}}\approx 0.85560}$
Central density2
Related polytopes
ArmySemi-uniform Twip, edge lengths ${\displaystyle {\frac {{\sqrt {6}}-{\sqrt {2}}}{2}}}$ (base), ${\displaystyle {\sqrt {{\sqrt {3}}-1}}}$ (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

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

• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}},\,\pm {\frac {\sqrt {{\sqrt {3}}-1}}{2}}\right),}$
• ${\displaystyle \left(\pm 1,\,0,\,\pm {\frac {\sqrt {{\sqrt {3}}-1}}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {\sqrt {3}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {{\sqrt {3}}-1}}{2}}\right),}$
• ${\displaystyle \left(0,\,\pm 1,\,\pm {\frac {\sqrt {{\sqrt {3}}-1}}{2}}\right).}$

## Variations

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.