# Pentagrammic prism

Pentagrammic prism
Rank3
TypeUniform
Notation
Bowers style acronymStip
Coxeter diagramx x5/2o ()
Elements
Faces5 squares, 2 pentagrams
Edges5+10
Vertices10
Vertex figureIsosceles triangle, edge lengths (5–1)/2, 2, 2
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {15-2{\sqrt {5}}}{20}}}\approx 0.72553}$
Volume${\displaystyle {\frac {\sqrt {25-10{\sqrt {5}}}}{4}}\approx 0.40615}$
Dihedral angles4–5/2: 90°
4–4: 36°
Height1
Central density2
Number of external pieces12
Level of complexity6
Related polytopes
ArmySemi-uniform Pip, edge lengths ${\displaystyle {\frac {{\sqrt {5}}-1}{2}}}$ (base), 1 (sides)
RegimentStip
DualPentagrammic tegum
ConjugatePentagonal prism
Convex corePentagonal prism
Abstract & topological properties
Flag count60
Euler characteristic2
OrientableYes
Genus0
Properties
SymmetryH2×A1, order 20
ConvexNo
NatureTame

The pentagrammic prism, or stip, is a prismatic uniform polyhedron. It consists of 2 pentagrams and 5 squares. Each vertex joins one pentagram and two squares. As the name suggests, it is a prism based on a pentagram.

## Vertex coordinates

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

• ${\displaystyle \left(\pm {\frac {1}{2}},\,-{\sqrt {\frac {5-2{\sqrt {5}}}{20}}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {{\sqrt {5}}-1}{4}},\,{\sqrt {\frac {5+{\sqrt {5}}}{40}}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left(0,\,-{\sqrt {\frac {5-{\sqrt {5}}}{10}}},\,\pm {\frac {1}{2}}\right).}$

## Related polyhedra

Two non-prismatic uniform polyhedron compounds are composed of pentagrammic prisms:

There are also an infinite amount of prismatic uniform compounds that are the prisms of compounds of pentagrams.