Decagrammic prism

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Decagrammic prism
Prism 10-3.png
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)
Circumradius7–25/2 ≈ 0.79496
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[edit | edit source]

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[edit | edit source]

A decagrammic prism has the following Coxeter diagrams:

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

Related polyhedra[edit | edit source]

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

External links[edit | edit source]