Pentagrammic prism

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Pentagrammic prism
Pentagrammic prism.png
Rank3
TypeUniform
SpaceSpherical
Bowers style acronymStip
Info
Coxeter diagramx x5/2o
SymmetryH2×A1, order 20
ArmySemi-uniform Pip
RegimentPip
Elements
Vertex figureIsosceles triangle, edge lengths (5–1)/2, 2, 2
Faces5 squares, 2 pentagrams
Edges5+10
Vertices10
Measures (edge length 1)
Circumradius(15–25)/20 ≈ 0.72553
Volume25–105/4 ≈ 0.40615
Dihedral angles4–5/2: 90°
 4–4: 36°
Height1
Central density2
Euler characteristic2
Related polytopes
DualPentagrammic bipyramid
ConjugatePentagonal prism
Convex corePentagonal prism
Properties
ConvexNo
OrientableYes
NatureTame

The pentagrammic prism, or stip, is a prismatic uniform polyhedron. It consists of 2 pentagrams and 5 squares. Each vertex joins one pentagram and two squares. As the name suggests, it is a prism based on a pentagram.

Vertex coordinates[edit | edit source]

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

  • (±1/2, –(5–25)/20, ±1/2),
  • (±(5–1)/4, (5+5)/40, ±1/2),
  • (0, –(5–5)/10, ±1/2).

Related polyhedra[edit | edit source]

Two non-prismatic uniform polyhedron compounds are composed of pentagrammic prisms:

There are also an infinite amount of prismatic uniform compounds that are the prisms of compounds of pentagrams.

External links[edit | edit source]