# Pentagonal-great heptagrammic duoprism

The pentagonal-great heptagrammic duoprism, also known as pagishdip or the 5-7/3 duoprism, is a uniform duoprism that consists of 7 pentagonal prisms and 5 great heptagrammic prisms, with two of each meeting at each vertex.

Pentagonal-great heptagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymPagishdip
Info
Coxeter diagramx5o x7/3o
SymmetryH2×I2(7), order 140
ArmySemi-uniform pheddip
RegimentPagishdip
Elements
Vertex figureDigonal disphenoid, edge lengths (1+5)/2 (base 1), 2cos(3π/7) (base 2), 2 (sides)
Cells7 pentagonal prisms, 5 great heptagrammic prisms
Faces35 squares, 7 pentagons, 5 great heptagrams
Edges35+35
Vertices35
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{5+\sqrt{5}}{10}+\frac{1}{4\sin^2\frac{3\pi}{7}}}≈0.99329}$
Hypervolume${\displaystyle \frac{7\sqrt{5(5+2\sqrt{5})}}{16\tan\frac{3\pi}{7}}≈0.68720}$
Dichoral anglesPip–5–pip: π/7 ≈ 25.71429°
Giship–7/3–giship: 108°
Pip–4–giship: 90°
Central density3
Related polytopes
DualPentagonal-great heptagrammic duotegum
ConjugatesPentagonal-heptagonal duoprism, Pentagonal-heptagrammic duoprism, Pentagrammic-heptagonal duoprism, Pentagrammic-heptagrammic duoprism, Pentagrammic-great heptagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame

## Vertex coordinates

The coordinates of a pentagonal-great heptagrammic duoprism, centered at the origin and with edge length 2sin(3π/7), are given by:

• (±sin(3π/7), –sin(3π/7)(5+25)/5, 1, 0),
• (±sin(3π/7), –sin(3π/7)(5+25)/5, cos(2π/7), ±sin(2π/7)),
• (±sin(3π/7), –sin(3π/7)(5+25)/5, cos(4π/7), ±sin(4π/7)),
• (±sin(3π/7), –sin(3π/7)(5+25)/5, cos(6π/7), ±sin(6π/7)),
• (±(1+5)sin(3π/7)/2, sin(3π/7)(5–5)/10, 1, 0),
• (±(1+5)sin(3π/7)/2, sin(3π/7)(5–5)/10, cos(2π/7), ±sin(2π/7)),
• (±(1+5)sin(3π/7)/2, sin(3π/7)(5–5)/10, cos(4π/7), ±sin(4π/7)),
• (±(1+5)sin(3π/7)/2, sin(3π/7)(5–5)/10, cos(6π/7), ±sin(6π/7)),
• (0, 2sin(3π/7)(5+5)/10, 1, 0),
• (0, 2sin(3π/7)(5+5)/10, cos(2π/7), ±sin(2π/7)),
• (0, 2sin(3π/7)(5+5)/10, cos(4π/7), ±sin(4π/7)),
• (0, 2sin(3π/7)(5+5)/10, cos(6π/7), ±sin(6π/7)).