Hexagrammic prism

Hexagrammic prism
(OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Coxeter diagram	xo3ox xx
Elements
Components	2 triangular prisms
Faces	6 squares, 4 triangles as 2 hexagrams
Edges	6+12
Vertices	12
Vertex figure	Isosceles triangle, edge lengths 1, √2, √2
Measures (edge length 1)
Circumradius	$\frac{\sqrt{21}}{6} ≈ 0.76376$
Volume	$\frac{\sqrt3}{2} ≈ 0.86603$
Dihedral angles	4–3: 90°
	4–4: 60°
Height	1
Central density	2
Number of external pieces	14
Level of complexity	6
Related polytopes
Army	Semi-uniform Hip
Regiment	*
Dual	Hexagrammic tegum
Conjugate	None
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	G2×A1, order 24
Convex	No
Nature	Tame

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:

• $\left(0,\,±\frac{\sqrt3}{3},\,±\frac12\right),$
• $\left(±\frac12,\,±\frac{\sqrt3}{6},\,±\frac12\right).$