# Pentagrammic-heptagonal duoprism

Pentagrammic-heptagonal duoprism
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymStahedip
Info
Coxeter diagramx5/2o x7o
SymmetryH2×I2(7), order 140
ArmySemi-uniform pheddip
RegimentStahedip
Elements
Vertex figureDigonal disphenoid, edge lengths (5–1)/2 (base 1), 2cos(π/7) (base 2), 2 (sides)
Cells7 pentagrammic prisms, 5 heptagonal prisms
Faces35 squares, 7 pentagrams, 5 heptagons
Edges35+35
Vertices35
Measures (edge length 1)
Circumradius$\sqrt{\frac{5–\sqrt{5}}{10}+\frac{1}{4\sin^2\frac{\pi}{7}}}≈1.26664$ Hypervolume$\frac{7\sqrt{5(5-2\sqrt{5})}}{16\tan\frac{\pi}{7}}≈1.47591$ Dichoral anglesStip–5/2–stip: 5π/7 ≈ 128.57143°
Hep–7–hep: 36°
Stip–4–hep: 90°
Central density2
Related polytopes
DualPentagrammic-heptagonal duotegum
ConjugatesPentagonal-heptagonal duoprism, Pentagonal-heptagrammic duoprism, Pentagonal-great heptagrammic duoprism, Pentagrammic-heptagrammic duoprism, Pentagrammic-great heptagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame

The pentagrammic-heptagonal duoprism, also known as stahedip or the 5/2-7 duoprism, is a uniform duoprism that consists of 7 pentagrammic prisms and 5 heptagonal prisms, with 2 of each meeting at each vertex.

## Vertex coordinates

The coordinates of a pentagrammic-heptagonal duoprism, centered at the origin and with edge length 2sin(π/7), are given by:

• (±sin(π/7), –sin(π/7)(5–2√5)/5, 1, 0),
• (±sin(π/7), –sin(π/7)(5–2√5)/5, cos(2π/7), ±sin(2π/7)),
• (±sin(π/7), –sin(π/7)(5–2√5)/5, cos(4π/7), ±sin(4π/7)),
• (±sin(π/7), –sin(π/7)(5–2√5)/5, cos(6π/7), ±sin(6π/7)),
• (±sin(π/7)(5–1)/2, sin(π/7)(5+√5)/10, 1, 0),
• (±sin(π/7)(5–1)/2, sin(π/7)(5+√5)/10, cos(2π/7), ±sin(2π/7)),
• (±sin(π/7)(5–1)/2, sin(π/7)(5+√5)/10, cos(4π/7), ±sin(4π/7)),
• (±sin(π/7)(5–1)/2, sin(π/7)(5+√5)/10, cos(6π/7), ±sin(6π/7)),
• (0, –2sin(π/7)(5–√5)/10, 1, 0),
• (0, –2sin(π/7)(5–√5)/10, cos(2π/7), ±sin(2π/7)),
• (0, –2sin(π/7)(5–√5)/10, cos(4π/7), ±sin(4π/7)),
• (0, –2sin(π/7)(5–√5)/10, cos(6π/7), ±sin(6π/7)).