# Pentagrammic-hexagonal duoprism

Pentagrammic-hexagonal duoprism
Rank4
TypeUniform
Notation
Bowers style acronymStahdip
Coxeter diagramx5/2o x6o ()
Elements
Cells6 pentagrammic prisms, 5 hexagonal prisms
Faces30 squares, 6 pentagrams, 5 hexagons
Edges30+30
Vertices30
Vertex figureDigonal disphenoid, edge lengths (5–1)/2 (base 1), 3 (base 2), 2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {15-{\sqrt {5}}}{10}}}\approx 1.12978}$
Hypervolume${\displaystyle {\frac {3{\sqrt {75-30{\sqrt {5}}}}}{8}}\approx 1.05521}$
Dichoral anglesStip–5/2–stip: 120°
Stip–4–hip: 90°
Hip–6–hip: 36°
Central density2
Number of external pieces16
Level of complexity12
Related polytopes
ArmySemi-uniform phiddip
RegimentStahdip
DualPentagrammic-hexagonal duotegum
ConjugatePentagonal-hexagonal duoprism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryH2×G2, order 120
ConvexNo
NatureTame

The pentagrammic-hexagonal duoprism, also known as stahdip or the 5/2-6 duoprism, is a uniform duoprism that consists of 6 pentagrammic prisms and 5 hexagonal prisms, with 2 of each at each vertex.

## Vertex coordinates

The coordinates of a pentagrammic-hexagonal duoprism, centered at the origin and with unit edge length, are given by:

• ${\displaystyle \left(\pm {\frac {1}{2}},\,-{\sqrt {\frac {5-2{\sqrt {5}}}{20}}},\,\pm 1,\,0\right),}$
• ${\displaystyle \left(\pm {\frac {1}{2}},\,-{\sqrt {\frac {5-2{\sqrt {5}}}{20}}},\,\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {{\sqrt {5}}-1}{4}},\,{\sqrt {\frac {5+{\sqrt {5}}}{40}}},\,\pm 1,\,0\right),}$
• ${\displaystyle \left(\pm {\frac {{\sqrt {5}}-1}{4}},\,{\sqrt {\frac {5+{\sqrt {5}}}{40}}},\,\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}}\right),}$
• ${\displaystyle \left(0,\,-{\sqrt {\frac {5-{\sqrt {5}}}{10}}},\,\pm 1,\,0\right),}$
• ${\displaystyle \left(0,\,-{\sqrt {\frac {5-{\sqrt {5}}}{10}}},\,\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}}\right).}$

## Representations

A pentagrammic-hexagonal duoprism has the following Coxeter diagrams:

• x5/2o x6o (full symmetry)
• x3x x5/2o () (A2×H2 symmetry, hexagons as ditrigons)