icosahedron

Clearly it must be that Saturn is a truncated icosahedron or similar.

I remember him joking that he has a recurring nightmare that he would meet a man in the street who could draw an icosahedron faster than him.

In the center of the stellated polyhedron there is an empty icosahedron.

Replying to myself: all those sides would be of equal length, defying Eculid -- or rather I'm missing the fact that five triangles meet in the original icosahedron.

There is nothing to differentiate the triangle of your icosahedron on the 0 meridian from its counterpart at 72, so they will all fall into the same relationship with the south pole.

For example, I could tell a rotating copper cube to become a glass icosahedron and reasonably expect to see my changes immediately reflected in the running program.

" To which Asimov responded "[that the teacher] may be imagining that because all theories are wrong, the earth may be thought spherical now, but cubical next century, and a hollow icosahedron the next, and a doughnut shape the one after.

Your strip of 10 triangles on the icosahedron: if that is indeed equatorial, then we have both latitudinal and longitudinal symmetry which renders your north and south hemispheres identical so things will match up.

By ordering the solids correctly—octahedron, icosahedron, dodecahedron, tetrahedron, and cube—Kepler found that the spheres correspond to the relative sizes of each planet's path around the Sun, generally varying from astronomical observations by less than 10%.