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Pentagrammic prism

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Uniform pentagrammic prism
Type Prismatic uniform polyhedron
Elements F = 7, E = 15
V = 10 (χ = 2)
Faces by sides 5{4}+2{5/2}
Schläfli symbol t{2,5/2} or {5/2}×{}
Wythoff symbol 2 5/2 | 2
Coxeter diagram
Symmetry D5h, [5,2], (*522), order 20
Rotation group D5, [5,2]+, (522), order 10
Index references U78(a)
Dual Pentagrammic dipyramid
Properties nonconvex

Vertex figure
4.4.5/2

In geometry, the pentagrammic prism is one in an infinite set of nonconvex prisms formed by square sides and two regular star polygon caps, in this case two pentagrams.

It has 7 faces, 15 edges and 10 vertices. This polyhedron is identified with the indexed name U78 as a uniform polyhedron.

It is a special case of a right prism with a pentagram as base, which in general has rectangular non-base faces.

Note that the pentagram face has an ambiguous interior because it is self-intersecting. The central pentagon region can be considered interior or exterior depending on how interior is defined. One definition of interior is the set of points that have a ray that crosses the boundary an odd number of times to escape the perimeter.

In either case, it is best to show the pentagram boundary line to distinguish it from a concave decagon.


An alternative representation with hollow centers to the pentagrams.
The pentagrammic dipyramid is the dual to the pentagrammic prism
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