Hexagonal-decagrammic duoprism

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Hexagonal-decagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymHistadedip
Info
Coxeter diagramx6o x10/3o
SymmetryG2×I2(10), order 240
ArmySemi-uniform hadedip
RegimentHistadedip
Elements
Vertex figureDigonal disphenoid, edge lengths 3 (base 1), (5–5)/2 (base 2), 2 (sides)
Cells10 hexagonal prisms, 6 decagrammic prisms
Faces60 squares, 10 hexagons, 6 decagrams
Edges60+60
Vertices60
Measures (edge length 1)
Circumradius(5–5)/2 ≈ 1.17557
Hypervolume153(5–25)/4 ≈ 4.71903
Dichoral anglesHip–6–hip: 72°
 Stiddip–10/3–stiddip: 120°
 Hip–4–stiddip: 90°
Central density3
Related polytopes
DualHexagonal-decagrammic duotegum
ConjugateHexagonal-decagonal duoprism
Properties
ConvexNo
OrientableYes
NatureTame


The hexagonal-decagramic duoprism, also known as histadedip or the 6-10/3 duoprism, is a uniform duoprism that consists of 10 hexagonal prisms and 6 decagrammic prisms, with 2 of each meeting at each vertex.

Vertex coordinates[edit | edit source]

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

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

External links[edit | edit source]