Pentagrammic crossed-antiprism

Template:Prism star polyhedron stat table File:Crossed pentagrammic antiprism.stl In geometry, the pentagrammic crossed-antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in this case two pentagrams.

It differs from the pentagrammic antiprism by having opposite orientations on the two pentagrams.

This polyhedron is identified with the indexed name U₈₀ as a uniform polyhedron.

An alternative representation with hollow pentagrams.

The pentagrammic crossed-antiprism may be inscribed within an icosahedron, and has ten triangular faces in common with the great icosahedron. It has the same vertex arrangement as the pentagonal antiprism. In fact, it may be considered as a parabidiminished great icosahedron.

Pentagrammic crossed-antiprism

Great icosahedron coloured with D5d symmetry

See also

• Prismatic uniform polyhedron

External links

• Weisstein, Eric W.. "Pentagrammic crossed antiprism". http://mathworld.wolfram.com/PentagrammicCrossedAntiprism.html. 
• http://www.mathconsult.ch/showroom/unipoly/80.html
• http://bulatov.org/polyhedra/uniform/u05.html
• https://web.archive.org/web/20050313234519/http://www.math.technion.ac.il/~rl/kaleido/data/05.html