Pentagrammic crossed-antiprism

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.

Uniform pentagrammic crossed-antiprism
TypePrismatic uniform polyhedron
ElementsF = 12, E = 20
V = 10 (χ = 2)
Faces by sides10{3}+2{5/2}
Schläfli symbols{2,10/3}
sr{2,5/3}
Wythoff symbol| 2 2 5/3
Coxeter diagram
=
SymmetryD5h, [5,2], (*522), order 20
Rotation groupD5, [5,2]+, (552), order 10
D5d
Index referencesU80(a)
DualPentagrammic concave trapezohedron
Propertiesnonconvex

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

  • 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
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