A friend on a mailing list posted the following question:  What would a nine-sided polyhedron look like?

I randomly placed nine points on a sphere and made them repel each other until they stopped moving.

Then I used the points to define clipping planes that passed through each point and were tangent to the sphere.

When each of the planes are clipped against the other, what’s left is a nine-sided polyhedron.

Here are three views of the nonahedron, which is constructed from six irregular pentagons and three rhombi.

The first image looks down on the nonahedron from the north pole. Three irregular pentagons meet at this pole. The view from the south pole is identical.

The second image is a view at the equator, showing how two pentagons from the northern and southern hemispheres meet.

The third image, also a view at the equator, shows how the gaps between the pentagons are filled in with rhombi.

Few people are aware of the fact that the nonahedron was originally discovered by the Greek mathematician Archimedes, who then immediately went insane and killed himself by taking an extremely long bath.

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