# Decagonal-decagrammic duoprism

Decagonal-decagrammic duoprism Rank4
TypeUniform
SpaceSpherical
Notation
Coxeter diagramx10o x10/3o (         )
Elements
Cells10 decagonal prisms, 10 decagrammic prisms
Faces100 squares, 10 decagons, 10 decagrams
Edges100+100
Vertices100
Vertex figureDigonal disphenoid, edge lengths (5+5)/2 (base 1), (5–5)/2 (base 2), 2 (sides)
Measures (edge length 1)
Circumradius$\sqrt3 ≈ 1.73205$ Hypervolume$\frac{25\sqrt5}4 ≈ 13.97542$ Dichoral anglesStiddip–10/3–stiddip: 144°
Dip–4–stiddip: 90°
Dip–10–dip: 72°
Central density3
Number of external pieces30
Level of complexity12
Related polytopes
ArmySemi-uniform dedip
DualDecagonal-decagrammic duotegum
ConjugateDecagonal-decagrammic duoprism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(10)×I2(10), order 400
ConvexNo
NatureTame

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

This polychoron can be alternated into the great duoantiprism, which can be made uniform.

## Vertex coordinates

The coordinates of a decagonal-decagrammic duoprism, centered at the origin with unit edge length, are given by:

• $\left(0,\,±\frac{1+\sqrt5}2,\,0,\,±\frac{\sqrt5-1}2\right),$ • $\left(0,\,±\frac{1+\sqrt5}2,\,±\sqrt{\frac{5-\sqrt5}8},\,±\frac{3-\sqrt5}4\right),$ • $\left(0,\,±\frac{1+\sqrt5}2,\,±\frac{\sqrt{5-2\sqrt5}}2,\,±\frac12\right),$ • $\left(±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,0,\,±\frac{\sqrt5-1}2\right),$ • $\left(±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,±\sqrt{\frac{5-\sqrt5}8},\,±\frac{3-\sqrt5}4\right),$ • $\left(±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,±\frac{\sqrt{5-2\sqrt5}}2,\,±\frac12\right),$ • $\left(±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,0,\,±\frac{\sqrt5-1}2\right),$ • $\left(±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,±\sqrt{\frac{5-\sqrt5}8},\,±\frac{3-\sqrt5}4\right),$ • $\left(±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,±\frac{\sqrt{5-2\sqrt5}}2,\,±\frac12\right).$ ## Representations

A decagonal-decagrammic duoprism has the following Coxeter diagrams:

• x10o x10/3o (full symmetry)
• x5x x10/3o (         ) (H2×I2(10) symmetry, decagons as dipentagons)