Pentagonal-decagrammic duoprism

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Pentagonal-decagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymPistadedip
Info
Coxeter diagramx5o x10/3o
SymmetryH2×I2(10), order 200
ArmySemi-uniform padedip
RegimentPistadedip
Elements
Vertex figureDigonal disphenoid, edge lengths (1+5)/2 (base 1), (5–5)/2 (base 2), 2 (sides)
Cells10 pentagonal prisms, 5 decagrammic prisms
Faces50 squares, 10 pentagons, 5 decagrams
Edges50+50
Vertices50
Measures (edge length 1)
Circumradius2(5–5)/5 ≈ 1.05146
Hypervolume25/8 = 3.125
Dichoral anglesPip–5–pip: 72°
 Stiddip–10/3–stiddip: 108°
 Pip–4–stiddip: 90°
Central density3
Related polytopes
DualPentagonal-decagrammic duotegum
ConjugatesPentagonal-decagonal duoprism, Pentagrammic-decagonal duoprism, Pentagrammic-decagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame


The pentagonal-decagrammic duoprism, also known as pistadedip or the 5-10/3 duoprism, is a uniform duoprism that consists of 10 pentagonal prisms and 5 decagrammic prisms, with two of each meeting at each vertex.

Vertex coordinates[edit | edit source]

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

  • (±1/2, –(5+25)/20, ±1/2, ±(5–25)/2),
  • (±1/2, –(5+25)/20, ±(3–5)/4, ±(5–5)/8),
  • (±1/2, –(5+25)/20, ±(5–1)/2, 0),
  • (±(1+5)/4, (5–5)/40, ±1/2, ±(5–25)/2),
  • (±(1+5)/4, (5–5)/40, ±(3–5)/4, ±(5–5)/8),
  • (±(1+5)/4, (5–5)/40, ±(5–1)/2, 0),
  • (0, (5+5)/10, ±1/2, ±(5–25)/2),
  • (0, (5+5)/10, ±(3–5)/4, ±(5–5)/8),
  • (0, (5+5)/10, ±(5–1)/2, 0).

External links[edit | edit source]