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}
Wythoff symbol	2 ⁵/₂ \| 2
Coxeter-Dynkin
Symmetry	D_5h
Index references	U_78(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.

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: 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.