# Heptagrammic-decagrammic duoprism

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Heptagrammic-decagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymShestadedip
Info
Coxeter diagramx7/2o x10/3o
SymmetryI2(7)×I2(10), order 280
ArmySemi-uniform hedadip
RegimentShestadedip
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(2π/7) (base 1), (5–5)/2 (base 2), 2 (sides)
Cells10 heptagrammic prisms, 7 decagrammic prisms
Faces70 squares, 10 heptagrams, 7 decagrams
Edges70+70
Vertices70
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{1}{4\sin^2\frac{2\pi}{7}}+\frac{3-\sqrt{5}}{2}}≈0.88936}$
Hypervolume${\displaystyle \frac{35\sqrt{5-2\sqrt{5}}}{8\tan\frac{2\pi}{7}}≈2.53487}$
Dichoral anglesShip–7/2–ship: 72°
Stiddip–10/3–stiddip: 3π/7 ≈ 77.14286°
Ship–4–stiddip: 90°
Central density6
Related polytopes
DualHeptagrammic-decagrammic duotegum
ConjugatesHeptagonal-decagonal duoprism, Heptagonal-decagrammic duoprism, Heptagrammic-decagonal duoprism, Great heptagrammic-decagonal duoprism, Great heptagrammic-decagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame

The heptagrammic-decagrammic duoprism, also known as shestadedip or the 7/2-10/3 duoprism, is a uniform duoprism that consists of 10 heptagrammic prisms and 7 decagrammic prisms, with 2 of each meeting at each vertex.

The name can also refer to the great heptagrammic-decagrammic duoprism.

## Vertex coordinates

The coordinates of a heptagrammic-decagrammic duoprism, centered at the origin and with edge length 2sin(2π/7), are given by:

• (1, 0, ±sin(2π/7), ±sin(2π/7)5–25),
• (1, 0, ±sin(2π/7)(3–5)/2, ±sin(2π/7)(5–5)/2),
• (1, 0, ±sin(2π/7)(5–1), 0),
• (cos(2π/7), ±sin(2π/7), ±sin(2π/7), ±sin(2π/7)5–25),
• (cos(2π/7), ±sin(2π/7), ±sin(2π/7)(3–5)/2, ±sin(2π/7)(5–5)/2),
• (cos(2π/7), ±sin(2π/7), ±sin(2π/7)(5–1), 0),
• (cos(4π/7), ±sin(4π/7), ±sin(2π/7), ±sin(2π/7)5–25),
• (cos(4π/7), ±sin(4π/7), ±sin(2π/7)(3–5)/2, ±sin(2π/7)(5–5)/2),
• (cos(4π/7), ±sin(4π/7), ±sin(2π/7)(5–1), 0),
• (cos(6π/7), ±sin(6π/7), ±sin(2π/7), ±sin(2π/7)5–25),
• (cos(6π/7), ±sin(6π/7), ±sin(2π/7)(3–5)/2, ±sin(2π/7)(5–5)/2),
• (cos(6π/7), ±sin(6π/7), ±sin(2π/7)(5–1), 0).