Hexagonal projection of the platonic solids

Posted by hexnet ::

In this diagram we see that four of the five platonic solids can be projected in two dimensions as hexagonally-symmetric figures. The hexahedron, octahedron, and icosahedron can all be orthographically projected as regular hexagons, and the dodecahedron can be so projected as a somewhat lopsided yet equal-angled hexagon (not shown), or as a hexagonally-symmetrical dodecagon (shown here). The tetrahedron—or "freak" polyhedron if you will—can of course be projected as an equilateral triangle, which although not truly hexagonal is still of the same general angular family.