STAR POLYHEDRON

In geometry, the term star polyhedron does not seem to have been properly defined, even though it is in common use. We can say that a star polyhedron is a polyhedron which has some repetitive quality of nonconvexity giving it a star-like visual quality.
There are two general kinds of star polyhedron:

★ Polyhedra which self-intersect in a repetitive way.

★ Concave polyhedra of a particular kind which alternate convex and concave or saddle vertices in a repetitive way.
Studies of star polyhedra are usually concerned with uniform and regular polyhedra. All these stars are of the self-intersecting kind. So some authorities might argue that the concave kind are not proper stars. But the latter usage seems so common that it cannot be ignored. The important thing is to be clear which kind you mean.

Contents

Uniform and regular star polyhedra

Star polytopes

See also

References

Uniform and regular star polyhedra

There are many uniform star polyhedra including two infinite series, of prisms and of antiprisms.
There are four regular star polyhedra, known as the Kepler-Poinsot polyhedra.

Star polytopes

Higher dimensional intersecting polytopes are called 'star polytopes'; for example, the 10 regular star polychora, called the Schläfli-Hess polychora.

See also

★ Star polygon

★ Stellation

★ Polyhedral compound

References

★ Coxeter, H.S.M., M.S. Longuet-Higgins and J.C.P Miller, Uniform Polyhedra, ''Phil. Trans.'' '246 A' (1954) pp. 401-450.

★ Coxeter, H.S.M., ''Regular Polytopes'', 3rd. ed., Dover Publications, 1973. ISBN 0-486-61480-8.