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.
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