# Pentagonal-heptagrammic duoprism

Pentagonal-heptagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymPashedip
Info
Coxeter diagramx5o x7/2o
SymmetryH2×I2(7), order 140
ArmySemi-uniform pheddip
RegimentPashedip
Elements
Vertex figureDigonal disphenoid, edge lengths (1+5)/2 (base 1), 2cos(2π/7) (base 2), 2 (sides)
Cells7 pentagonal prisms, 5 heptagrammic prisms
Faces35 squares, 7 pentagons, 5 heptagrams
Edges35+35
Vertices35
Measures (edge length 1)
Circumradius$\sqrt{\frac{5+\sqrt{5}}{10}+\frac{1}{4\sin^2\frac{2\pi}{7}}}≈1.06424$ Hypervolume$\frac{7\sqrt{5(5+2\sqrt{5})}}{16\tan\frac{2\pi}{7}}≈2.40106$ Dichoral anglesPip–5–pip: 3π/7 ≈ 77.14286°
Ship–7/2–ship: 108°
Pip–4–ship: 90°
Central density2
Related polytopes
DualPentagonal-heptagrammic duotegum
ConjugatesPentagonal-heptagonal duoprism, Pentagonal-great heptagrammic duoprism, Pentagrammic-heptagonal duoprism, Pentagrammic-heptagrammic duoprism, Pentagrammic-great heptagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame

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

The name can also refer to the pentagonal-great heptagrammic duoprism.

## Vertex coordinates

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

• (±sin(2π/7), –sin(2π/7)(5+25)/5, 1, 0),
• (±sin(2π/7), –sin(2π/7)(5+25)/5, cos(2π/7), ±sin(2π/7)),
• (±sin(2π/7), –sin(2π/7)(5+25)/5, cos(4π/7), ±sin(4π/7)),
• (±sin(2π/7), –sin(2π/7)(5+25)/5, cos(6π/7), ±sin(6π/7)),
• (±(1+5)sin(2π/7)/2, sin(2π/7)(5–5)/10, 1, 0),
• (±(1+5)sin(2π/7)/2, sin(2π/7)(5–5)/10, cos(2π/7), ±sin(2π/7)),
• (±(1+5)sin(2π/7)/2, sin(2π/7)(5–5)/10, cos(4π/7), ±sin(4π/7)),
• (±(1+5)sin(2π/7)/2, sin(2π/7)(5–5)/10, cos(6π/7), ±sin(6π/7)),
• (0, 2sin(2π/7)(5+5)/10, 1, 0),
• (0, 2sin(2π/7)(5+5)/10, cos(2π/7), ±sin(2π/7)),
• (0, 2sin(2π/7)(5+5)/10, cos(4π/7), ±sin(4π/7)),
• (0, 2sin(2π/7)(5+5)/10, cos(6π/7), ±sin(6π/7)).