Pentagrammic prism

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

3D model of a (uniform) pentagrammic prism

In geometry, the pentagrammic prism is one of 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.

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 the interior is defined. One definition of the interior is the set of points that have a ray that crosses the boundary an odd number of times to escape the perimeter.

Gallery

An alternative representation with hollow centers to the pentagrams.

The pentagrammic dipyramid is the dual to the pentagrammic prism.

External links

• Weisstein, Eric W. "Pentagrammic prism". MathWorld.
• Weisstein, Eric W. "Pentagrammic dipyramid". MathWorld.
• http://www.mathconsult.ch/showroom/unipoly/78.html
• http://bulatov.org/polyhedra/uniform/u03.html
• Paper model of pentagrammic prism
• https://web.archive.org/web/20050313234702/http://www.math.technion.ac.il/~rl/kaleido/data/03.html
• http://home.comcast.net/~tpgettys/nonconvexprisms.html
• https://web.archive.org/web/20060211140715/http://www.ac-noumea.nc/maths/amc/polyhedr/no_conv5_.htm
• Paper Model (net) Pentagrammic Prism