# Pentagonal-heptagonal duoprism

(Redirected from 7-5 duoprism)
Pentagonal-heptagonal duoprism Rank4
TypeUniform
SpaceSpherical
Bowers style acronymPheddip
Info
Coxeter diagramx5o x7o
SymmetryH2×I2(7), order 140
ArmyPheddip
RegimentPheddip
Elements
Vertex figureDigonal disphenoid, edge lengths (1+5)/2 (base 1), 2cos(π/7) (base 2), and 2 (sides)
Cells7 pentagonal prisms, 5 heptagonal prisms
Faces35 squares, 7 pentagons, 5 heptagons
Edges35+35
Vertices35
Measures (edge length 1)
Circumradius$\sqrt{\frac{5+\sqrt5}{10}+\frac{1}{4\sin^2\frac\pi7}} ≈ 1.43234$ Hypervolume$\frac{7\sqrt{25+10\sqrt5}}{16\tan\frac\pi7} ≈ 6.25206$ Dichoral anglesPip–5–pip: $\frac{5\pi}{7} ≈ 128.57143°$ Hep–7–hep: 108°
Pip–4–hep: 90°
Central density1
Euler characteristic0
Number of pieces12
Level of complexity6
Related polytopes
DualPentagonal-heptagonal duotegum
ConjugatesPentagonal-heptagrammic duoprism, Pentagonal-great heptagrammic duoprism, Pentagrammic-heptagonal duoprism, Pentagrammic-heptagrammic duoprism, Pentagrammic-great heptagrammic duoprism
Properties
ConvexYes
OrientableYes
NatureTame

The pentagonal-heptagonal duoprism or pheddip, also known as the 5-7 duoprism, is a uniform duoprism that consists of 5 heptagonal prisms and 7 pentagonal prisms, with two of each joining at each vertex.

## Vertex coordinates

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

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