Pentagrammic crossed-antiprism

Uniform pentagrammic crossed-antiprism
Type Prismatic uniform polyhedron
Elements F = 12, E = 20
V = 10 (χ = 2)
Faces by sides 10{3}+2{5/2}
Schläfli symbol s{2,10/3}
sr{2,5/3}
Wythoff symbol | 2 2 5/3
Coxeter diagram
=
Symmetry D5h, [5,2], (*522), order 20
Rotation group D5, [5,2]+, (552), order 10
D5d
Index references U80(a)
Dual Pentagrammic concave trapezohedron
Properties nonconvex

Vertex figure
3.3.3.5/3 or 3.3.3.-5/2

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.

3D model of a (uniform) pentagrammic crossed-antiprism

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

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  • Weisstein, Eric W. "Pentagrammic crossed antiprism". MathWorld.
  • 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