Pentagrammic prism

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Uniform Pentagrammic prism
Pentagrammic prism.png
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}x{}
Wythoff symbol 2 5/2 | 2
Coxeter diagram CDel node 1.pngCDel 5.pngCDel rat.pngCDel d2.pngCDel node.pngCDel 2.pngCDel node 1.png
Symmetry D5h, [5,2], (*522), order 20
Rotation group D5, [5,2]+, (522), order 10
Index references U78(a)
Dual Pentagrammic dipyramid
Properties nonconvex
Pentagrammic prism vertfig.png
Vertex figure

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 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.


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

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