The 72 faces of this polyhedron are all pentagons. Twelve are regular, while the other sixty are not. Something I do not know, but would like to find out: is 72 the maximum number of faces a convex polyhedron can have, if all its faces must be convex pentagons?

[Update: 72 is not the maximum, as was explained to me on Facebook. I’ll try to find ways to generate images of more all-pentagon polyhedra, with more faces, for future posts here.]

Side note: this is the 1000th post on this blog. To all who follow and comment, thank you.

The program I use for these polyhedral investigations is *Stella 4d*, available at www.software3d.com/Stella.php.

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where does the “kai” in the name come from?

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It’s Greek for “and.”

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OK, disregard previous question is it not heptacontrakaidohedron?

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I’ve seen both systems used. As far as I know, there’s no universally agreed-upon naming system for polyhedra by number of faces. There are a lot of names out there, and sometimes they “bump into” each other.

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