# Decagrammic prism

Decagrammic prism Rank3
TypeUniform
SpaceSpherical
Bowers style acronymStiddip
Info
Coxeter diagramx x10/3o
SymmetryI2(10)×A1, order 40
ArmySemi-uniform Dip
RegimentStiddip
Elements
Vertex figureIsosceles triangle, edge lengths 2, 2, (5–5)/2
Faces10 squares, 2 decagrams
Edges10+20
Vertices20
Measures (edge length 1)
Volume55–25/2 ≈ 1.81636
Dihedral angles4–10/3: 90°
4–4: 72°
Height1
Central density3
Euler characteristic2
Related polytopes
DualDecagrammic bipyramid
ConjugateDecagonal prism
Properties
ConvexNo
OrientableYes
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:

• (±1/2, ±(5–25)/2, ±1/2),
• (±(3–5)/4, ±(5–5)/8, ±1/2),
• (±(5–1)/2, 0, ±1/2).

## 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.