# Hexagrammic prism

Hexagrammic prism
Rank3
TypeUniform
Notation
Coxeter diagramxo3ox xx
Elements
Components2 triangular prisms
Faces6 squares, 4 triangles as 2 hexagrams
Edges6+12
Vertices12
Vertex figureIsosceles triangle, edge lengths 1, 2, 2
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {21}}{6}}\approx 0.76376}$
Volume${\displaystyle {\frac {\sqrt {3}}{2}}\approx 0.86603}$
Dihedral angles4–3: 90°
4–4: 60°
Height1
Central density2
Number of external pieces14
Level of complexity6
Related polytopes
ArmySemi-uniform Hip, edge lengths ${\displaystyle {\frac {\sqrt {3}}{3}}}$ (base), 1 (sides)
Regiment*
DualHexagrammic tegum
ConjugateNone
Abstract & topological properties
Flag count72
OrientableYes
Properties
SymmetryG2×A1, order 24
ConvexNo
NatureTame

The hexagrammic prism or compound of 2 triangular prisms is a prismatic uniform polyhedron compound. It consists of 2 hexagrams and 6 squares. Each vertex joins one hexagram and two squares. As the name suggests, it is a prism based on a hexagram.

Its quotient prismatic equivalent is the octahedral prism, which is four-dimensional.

## Vertex coordinates

A hexagrammic prism of edge length 1 has vertex coordinates given by:

• ${\displaystyle \left(0,\,\pm {\frac {\sqrt {3}}{3}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{6}},\,\pm {\frac {1}{2}}\right).}$

## Variations

This compound has variants where the bases are non-regular compounds of two triangles. In these cases the compound has only triangular prismatic symmetry and the convex hull is a ditrigonal prism.