NONCONVEX UNIFORM POLYHEDRON

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In geometry, a nonconvex uniform polyhedron, or ''uniform star polyhedron'', is a self-intersecting uniform polyhedron. It can contain either ''nonconvex polygon'' faces, ''nonconvex vertex figures'' or both.
The complete set of 57 nonprismatic uniform star polyhedra includes the 4 regular ones, called the Kepler-Poinsot polyhedra.
There are also two infinite sets of ''uniform star prisms'' and ''uniform star antiprisms''.
Here are two example ''star polyhedra'', the first with five pentagram faces per vertex in a pentagonal vertex figure, and second with five triangles per vertex in a pentagrammic vertex figure:

small stellated dodecahedron Nonconvex faces: ''5/2.5/2.5/2.5/2.5/2'' vertex figure

Great icosahedron Nonconvex vertex figure: ''(3.3.3.3.3)/2''

Contents

See also

Reference

See also

★ Star polygon

★ list of uniform polyhedra

Reference

★ Uniform Polyhedra, , H. S. M., Coxeter, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences,

★ Polyhedron Models, , Magnus, Wenninger, Cambridge University Press, 1974, ISBN 0-521-09859-9