Pentagonal-octagrammic duoprism

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Pentagonal-octagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymPistodip
Info
Coxeter diagramx5o x8/3o
SymmetryH2×I2(8), order 160
ArmySemi-uniform podip
RegimentPistodip
Elements
Vertex figureDigonal disphenoid, edge lengths (1+5)/2 (base 1), 2–2 (base 2), 2 (sides)
Cells8 pentagonal prisms, 5 octagrammic prisms
Faces40 squares, 8 pentagons, 5 octagrams
Edges40+40
Vertices40
Measures (edge length 1)
Circumradius(15+5–52)/10 ≈ 1.00822
Hypervolume5(5+25)(2–1)/2 ≈ 1.42529
Dichoral anglesPip–5–pip: 45°
 Stop–8/3–stop: 108°
 Pip–4–stop: 90°
Central density3
Related polytopes
DualPentagonal-octagrammic duotegum
ConjugatesPentagonal-octagonal duoprism, Pentagrammic-octagonal duoprism, Pentagrammic-octagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame


The pentagonal-octagrammic duoprism, also known as pistodip or the 5-8/3 duoprism, is a uniform duoprism that consists of 8 pentagonal prisms and 5 octagrammic prisms, with 2 of each meeting at each vertex.

Vertex coordinates[edit | edit source]

The coordinates of a pentagonal-octagrammic duoprism, centered at the origin and with edge length 1, are given by:

  • (±(2–1)/2, ±1/2, ±1/2, –(5+25)/20),
  • (±(2–1)/2, ±1/2, ±(1+5)/4, (5–5)/40),
  • (±(2–1)/2, ±1/2, 0, (5+5)/10),
  • (±1/2, ±(2–1)/2, ±1/2, –(5+25)/20),
  • (±1/2, ±(2–1)/2, ±(1+5)/4, (5–5)/40),
  • (±1/2, ±(2–1)/2, 0, (5+5)/10).

External links[edit | edit source]