Hexagrammic prism

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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
Volume
Dihedral angles4–3: 90°
 4–4: 60°
Height1
Central density2
Number of external pieces14
Level of complexity6
Related polytopes
ArmySemi-uniform Hip, edge lengths (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[edit | edit source]

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

Variations[edit | edit source]

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.