# Decagrammic duoprism

Decagrammic duoprism Rank4
TypeUniform
SpaceSpherical
Notation
Coxeter diagramx10/3o x10/3o (           )
Elements
Cells20 decagrammic prisms
Faces100 squares, 20 decagrams
Edges200
Vertices100
Vertex figureTetragonal disphenoid, edge lengths (5–5)/2 (bases) and 2 (sides)
Measures (edge length 1)
Circumradius$\frac{\sqrt{10}-\sqrt2}{2} ≈ 0.87403$ Inradius$\frac{\sqrt{5-2\sqrt5}}{2} ≈ 0.36327$ Hypervolume$25\frac{5-2\sqrt5}{4} ≈ 3.29915$ Dichoral anglesStiddip–4–stiddip: 90°
Stiddip–10/3–stiddip: 72°
Central density9
Number of external pieces40
Level of complexity12
Related polytopes
ArmyDedip
DualDecagrammic duotegum
ConjugateDecagonal duoprism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(10)≀S2, order 800
ConvexNo
NatureTame

The decagrammic duoprism or stadidip, also known as the decagrammic-decagrammic duoprism, the 10/3 duoprism or the 10/3-10/3 duoprism, is a noble uniform duoprism that consists of 20 decagrammic prisms, with 4 meeting at each vertex.

A unit decagrammic duoprism can be vertex-inscribed into a grand ditetrahedronary hexacosidishecatonicosachoron.

## Vertex coordinates

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

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