pentagrammic crossed antiprism on:
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geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, the pentagrammic crossed-antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon
In geometry, a star polygon is a type of non-convex polygon. Regular star polygons have been studied in depth; while star polygons in general appear not to have been formally defined, certain notable ones can arise through truncation operations ...
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.
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.
See also
* Prismatic uniform polyhedronExternal links
* *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 Prismatoid polyhedra {{Polyhedron-stub