# Enneagonal-dodecagrammic duoprism

(Redirected from 12/5-9 duoprism)
Enneagonal-dodecagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx9o x12/5o
SymmetryI2(9)×I2(12), order 432
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(π/9) (base 1), (62)/2 (base 2), 2 (sides)
Cells12 enneagonal prisms, 9 dodecagrammic prisms
Faces108 squares, 12 enneagons, 9 dodecagrams
Edges108+108
Vertices108
Measures (edge length 1)
Circumradius$\sqrt{\frac{1}{4\sin^2\frac{\pi}{9}}+2-\sqrt{3}}≈1.55084$ Hypervolume$\frac{27(2-\sqrt{3})}{4\tan\frac{\pi}{9}}≈4.96924$ Dichoral anglesEp–9–ep: 30°
12/5p–12/5–12/5p: 140°
Ep–4–12/5p: 90°
Central density5
Related polytopes
DualEnneagonal-dodecagrammic duotegum
ConjugatesEnneagonal-dodecagonal duoprism, Enneagrammic-dodecagonal duoprism, Enneagrammic-dodecagrammic duoprism, Great enneagrammic-dodecagonal duoprism, Great enneagrammic-dodecagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame

The enneagonal-dodecagrammic duoprism, also known as the 9-12/5 duoprism, is a uniform duoprism that consists of 12 enneagonal prisms and 9 dodecagrammic prisms, with 2 of each meeting at each vertex.

## Vertex coordinates

The coordinates of a enneagonal-dodecagrammic duoprism, centered at the origin and with edge length 2sin(π/9), are given by:

• (1, 0, ±sin(π/9)(3–1), ±sin(π/9)(3–1)),
• (1, 0, ±sin(π/9), ±sin(π/9)(2–3)),
• (1, 0, ±sin(π/9)(2–3), ±sin(π/9)),
• (cos(2π/9), ±sin(2π/9), ±sin(π/9)(3–1), ±sin(π/9)(3–1)),
• (cos(2π/9), ±sin(2π/9), ±sin(π/9), ±sin(π/9)(2–3)),
• (cos(2π/9), ±sin(2π/9), ±sin(π/9)(2–3), ±sin(π/9)),
• (cos(4π/9), ±sin(4π/9), ±sin(π/9)(3–1), ±sin(π/9)(3–1)),
• (cos(4π/9), ±sin(4π/9), ±sin(π/9), ±sin(π/9)(2–3)),
• (cos(4π/9), ±sin(4π/9), ±sin(π/9)(2–3), ±sin(π/9)),
• (–1/2, ±3/2, ±sin(π/9)(3–1), ±sin(π/9)(3–1)),
• (–1/2, ±3/2, ±sin(π/9), ±sin(π/9)(2–3)),
• (–1/2, ±3/2, ±sin(π/9)(2–3), ±sin(π/9)),
• (cos(8π/9), ±sin(8π/9), ±sin(π/9)(3–1), ±sin(π/9)(3–1)),
• (cos(8π/9), ±sin(8π/9), ±sin(π/9), ±sin(π/9)(2–3)),
• (cos(8π/9), ±sin(8π/9), ±sin(π/9)(2–3), ±sin(π/9)).