Pentagrammic duoprism

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Pentagrammic duoprism
5-2-5-2 duoprism.png
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymStardip
Info
Coxeter diagramx5/2o x5/2o
SymmetryH2≀S2, order 200
ArmyPedip
RegimentStardip
Elements
Vertex figureTetragonal disphenoid, edge lengths (5–1)/2 (bases) and 2 (sides)
Cells10 pentagrammic prisms
Faces25 squares, 10 pentagrams
Edges50
Vertices25
Measures (edge length 1)
Circumradius(5–5)/5 ≈ 0.74350
Inradius(5–25)/20 ≈ 0.16246
Hypervolume5(5–25)/16 ≈ 0.16496
Dichoral anglesStip–5/2-stip: 36°
 Stip–4–stip: 90°
Central density4
Related polytopes
DualPentagrammic duotegum
ConjugatePentagonal duoprism
Properties
ConvexNo
OrientableYes
NatureTame


The pentagrammic duoprism or stardip, also known as the pentagrammic-pentagrammic duoprism, the 5/2 duoprism or the 5/2-5/2 duoprism, is a noble uniform duoprism that consists of 10 pentagrammic prisms and 25 vertices.

Vertex coordinates[edit | edit source]

The coordinates of a pentagrammic duoprism of edge length 1, centered at the origin, are given by:

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

External links[edit | edit source]