# Heptagonal-decagrammic duoprism

(Redirected from 7-10/3 duoprism)
Heptagonal-decagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx7o x10/3o
SymmetryI2(7)×I2(10), order 280
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(π/7) (base 1), (5–5)/2 (base 2), 2 (sides)
Cells10 heptagonal prisms, 7 decagrammic prisms
Faces70 squares, 10 heptagons, 7 decagrams
Edges70+70
Vertices70
Measures (edge length 1)
Circumradius$\sqrt{\frac{1}{4\sin^2\frac{\pi}{7}}+\frac{3–\sqrt{5}}{2}}≈1.30765$ Hypervolume$\frac{35\sqrt{5-2\sqrt{5}}}{8\tan\frac{\pi}{7}}≈6.60048$ Dichoral anglesHep–7–hep: 72°
Stiddip–10/3–stiddip: 5π/7 ≈ 128.57143°
Hep–4–stiddip: 90°
Central density3
Related polytopes
DualHeptagonal-decagrammic duotegum
ConjugatesHeptagonal-decagonal duoprism, Heptagrammic-decagonal duoprism, Heptagrammic-decagrammic duoprism, Great heptagrammic-decagonal duoprism, Great heptagrammic-decagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame

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

## Vertex coordinates

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

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