Polyhedron 666

This shape represents a regular polyhedron which is denoted, somewhat apocalyptically, {6,6}_6 (and thus, "Polyhedron 666").  This means that the 2-dimensional faces are hexagons, meeting 6 per vertex, and such that the Petrie polygons are also hexagons.  This is also an example of a regular polyhedron of index 2.  Having 20 vertices, 60 edges, and 20 2-dimensional faces, this polyhedron is, somewhat ominously, self-dual in a way that is similar to the way that the regular tetrahedron is self-dual.  Since the underlying surface is orientable, this represents a surface of genus 9.  (9 is 6 upside down, don't forget.)  One may also identify this shape with a stellation of the regular icosahedron.  Available in red or heavy metal.