# Decagrammic prism

Decagrammic prism Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymStiddip
Coxeter diagramx x10/3o (       )
Elements
Faces10 squares, 2 decagrams
Edges10+20
Vertices20
Vertex figureIsosceles triangle, edge lengths 2, 2, (5–5)/2
Measures (edge length 1)
Circumradius$\frac{\sqrt{7-2\sqrt5}}{2} ≈ 0.79496$ Volume$\frac{5\sqrt{5-2\sqrt5}}{2} ≈ 1.81636$ Dihedral angles4–10/3: 90°
4–4: 72°
Height1
Central density3
Number of pieces22
Level of complexity6
Related polytopes
ArmySemi-uniform Dip
RegimentStiddip
DualDecagrammic tegum
ConjugateDecagonal prism
Convex coreDecagonal prism
Abstract properties
Euler characteristic2
Topological properties
OrientableYes
Properties
SymmetryI2(10)×A1, order 40
ConvexNo
NatureTame

The decagrammic prism, or stiddip, is a prismatic uniform polyhedron. It consists of 2 decagrams and 10 squares. Each vertex joins one decagram and two squares. As the name suggests, it is a prism based on a decagram.

## Vertex coordinates

A decagrammic prism of edge length 1 has vertex coordinates given by:

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

A decagrammic prism has the following Coxeter diagrams:

• x x10/3o (full symmetry)
• x x5/3x (base with H2 symmetry)

## Related polyhedra

The great rhombisnub dodecahedron is a uniform polyhedron compound composed of 6 decagrammic prisms.