Polyhedral planets

This interesting article describes several hypothetical cubical worlds-- a hypothesized Planet X from 1884; a world of chimeric creatures called Aocicinori (illustrated in tracts handed out at Rice University, Texas, by a "mysterious, well-dressed gentleman" and created by a mental patient); and a cubical version of our own Earth:

Contemporary cosmologist Karen L. Masters also finds the topic of cube worlds fascinating -- especially the atmospheric possibilities. As she explains in Cornell's Ask a Physicist feature, all six faces of the [planet] would boast temperate weather, centralized bodies of water and none of them would feature polar or equatorial weather. What's more, the pointy edges of the cube would actually poke through the planet's atmosphere like titanic mountains.

 I am reminded of the far-future tetrahedral Earth described in a magazine article from 1918:

The world is now the shape of a globe, the shape which gives the biggest possible bulk for its surface, but the inside of the earth is still cooling and condensing, and the internal changes are slowly changing its shape. The surface, already condensed to its utmost, will not change with the core; it cannot reduce its area, but it adapts itself to the shrinking interior by taking a shape which occupies less bulk. So the earth is to become a tetrahedron, a sort of pyramid, the shape which gives the smallest bulk for its surface. Let us think about it all.