Pentagrammic prism

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.

Uniform Pentagrammic prism
TypePrismatic uniform polyhedron
ElementsF = 7, E = 15
V = 10 (χ = 2)
Faces by sides5{4}+2{5/2}
Schläfli symbolt{2,5/2} or {5/2}x{}
Wythoff symbol2 5/2 | 2
Coxeter diagram
SymmetryD5h, [5,2], (*522), order 20
Rotation groupD5, [5,2]+, (522), order 10
Index referencesU78(a)
DualPentagrammic dipyramid
Propertiesnonconvex

Vertex figure
4.4.5/2

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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