Decagonal-dodecagrammic duoprism

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Decagonal-dodecagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx10o x12/5o
SymmetryI2(10)×I2(12), order 480
ArmySemi-uniform datwadip
Elements
Vertex figureDigonal disphenoid, edge lengths (5+5)/2 (base 1), (62)/2 (base 2), 2 (sides)
Cells12 decagonal prisms, 10 dodecagrammic prisms
Faces120 squares, 12 decagons, 10 dodecagrams
Edges120+120
Vertices120
Measures (edge length 1)
Circumradius(7+5–23)/2 ≈ 1.69882
Hypervolume15(2–3)5+25/2 ≈ 6.18497
Dichoral anglesDip–10–dip: 30°
 12/5p–12/5–12/5p: 144°
 Dip–4–12/5p: 90°
Central density5
Related polytopes
DualDecagonal-dodecagrammic duotegum
ConjugatesDecagonal-dodecagonal duoprism, Decagrammic-dodecagonal duoprism, Decagrammic-dodecagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame


The decagonal-dodecagrammic duoprism, also known as the 10-12/5 duoprism, is a uniform duoprism that consists of 12 decagonal prisms and 10 dodecagrammic prisms, with 2 of each meeting at each vertex.

Vertex coordinates[edit | edit source]

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

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

External links[edit | edit source]