Pentagrammic-heptagonal duoprism

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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
Hypervolume
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[edit | edit source]

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)).

External links[edit | edit source]