A Pentagonal Dokaiheptacontahedron

pentagonal dokaiheptacontahedrongifThe 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.

4 thoughts on “A Pentagonal Dokaiheptacontahedron

    • 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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