In geometry, a uniform star polyhedron is a self-intersecting uniform polyhedron. They are also sometimes called nonconvex polyhedra to imply self-intersecting. Each polyhedron can contain either star polygon faces, star polygon vertex figures, or both.
A display of uniform polyhedra at the Science Museum in London
In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive. It follows that all vertices are congruent.
Platonic solid: Tetrahedron
Image: Tetrakishexahedron
Image: Disdyakisdodecahedron
Image: Disdyakistriacontahedron