# Decagrammic prism

Decagrammic prism
Rank3
TypeUniform
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${\displaystyle {\frac {\sqrt {7-2{\sqrt {5}}}}{2}}\approx 0.79496}$
Volume${\displaystyle {\frac {5{\sqrt {5-2{\sqrt {5}}}}}{2}}\approx 1.81636}$
Dihedral angles4–10/3: 90°
4–4: 72°
Height1
Central density3
Number of external pieces22
Level of complexity6
Related polytopes
ArmySemi-uniform Dip, edge lengths ${\displaystyle {\frac {3-{\sqrt {5}}}{2}}}$ (base), 1 (sides)
RegimentStiddip
DualDecagrammic tegum
ConjugateDecagonal prism
Convex coreDecagonal prism
Abstract & topological properties
Flag count120
Euler characteristic2
OrientableYes
Genus0
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:

• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {5-2{\sqrt {5}}}}{2}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\sqrt {\frac {5-{\sqrt {5}}}{8}}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {{\sqrt {5}}-1}{2}},\,0,\,\pm {\frac {1}{2}}\right).}$

## 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.