Pentagrammic prism

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Pentagrammic prism
Pentagrammic prism.png
Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymStip
Coxeter diagramx x5/2o (CDel node 1.pngCDel 2.pngCDel node 1.pngCDel 5.pngCDel rat.pngCDel 2x.pngCDel node.png)
Elements
Faces5 squares, 2 pentagrams
Edges5+10
Vertices10
Vertex figureIsosceles triangle, edge lengths (5–1)/2, 2, 2
Measures (edge length 1)
Circumradius
Volume
Dihedral angles4–5/2: 90°
 4–4: 36°
Height1
Central density2
Number of pieces12
Level of complexity6
Related polytopes
ArmySemi-uniform Pip
RegimentStip
DualPentagrammic tegum
ConjugatePentagonal prism
Convex corePentagonal prism
Abstract properties
Euler characteristic2
Topological properties
OrientableYes
Properties
SymmetryH2×A1, order 20
ConvexNo
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:

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]