# Great heptagrammic-decagrammic duoprism

Great heptagrammic-decagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx7/3o x10/3o
SymmetryI2(7)×I2(10), order 280
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(3π/7) (base 1), (5–5)/2 (base 2), 2 (sides)
Cells10 great heptagrammic prisms, 7 decagrammic prisms
Faces70 squares, 10 great heptagrams, 7 decagrams
Edges70+70
Vertices70
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{1}{4\sin^2\frac{3\pi}{7}}+\frac{3-\sqrt{5}}{2}}≈0.80311}$
Hypervolume${\displaystyle \frac{35\sqrt{5-2\sqrt{5}}}{8\tan\frac{3\pi}{7}}≈0.72550}$
Dichoral anglesGiship–7/3–giship: 72°
Stiddip–10/3–stiddip: π/7 ≈ 25.71429°
Giship–4–stiddip: 90°
Central density9
Related polytopes
DualGreat heptagrammic-decagrammic duotegum
ConjugatesHeptagonal-decagonal duoprism, Heptagonal-decagrammic duoprism, Heptagrammic-decagonal duoprism, Heptagrammic-decagrammic duoprism, Great heptagrammic-decagonal duoprism
Properties
ConvexNo
OrientableYes
NatureTame

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

## Vertex coordinates

The coordinates of a great heptagrammic-decagrammic duoprism, centered at the origin and with edge length 2sin(3π/7), are given by:

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