Decagrammic-dodecagrammic duoprism

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Decagrammic-dodecagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx10/3o 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 decagrammic prisms, 10 dodecagrammic prisms
Faces12 decagrams, 10 dodecagrams, 120 squares
Edges120+120
Vertices120
Measures (edge length 1)
Circumradius(7–5–23)/2 ≈ 0.80617
Hypervolume155–25(2–3)/2 ≈ 1.46007
Dichoral anglesStiddip–10/3–stiddip: 30°
 12/5p–12/5–12/5p: 72°
 Stiddip–4–12/5p: 90°
Central density15
Related polytopes
DualDecagrammic-dodecagrammic duotegum
ConjugatesDecagonal-dodecagonal duoprism, Decagonal-dodecagrammic duoprism, Decagrammic-dodecagonal duoprism
Properties
ConvexNo
OrientableYes
NatureTame


The decagrammic-dodecagrammic duoprism, also known as the 10/3-12/5 duoprism, is a uniform duoprism that consists of 12 decagrammic prisms and 10 dodecagrammic prisms, with 2 of each meeting at each vertex.

Coordinates[edit | edit source]

The vertex coordinates of a decagrammic-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),
  • (±(5–1)/2, 0, ±(3–1)/2, ±(3–1)/2),
  • (±(5–1)/2, 0, ±1/2, ±(2–3)/2),
  • (±(5–1)/2, 0, ±(2–3)/2, ±1/2).

External links[edit | edit source]