Category Archives: Mathematics

The dominant topic of my blog. You figured that out from the blog’s name, though, right?

Four Polyhedra Featuring Heptagons

Heptagons only appear infrequently in interesting polyhedra. I recently found a few that I like. To form the first of these solids, shown above, I started with the icosidodecahedron, dropped the symmetry of the model from icosahedral to tetrahedral, and … Continue reading

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A Pyritohedral, Stellated Polyhedron, and Its Convex Hull

To make this polyhedron using Stella 4d (available here), I began with the dodecahedron, dropped the symmetry of the model from icosahedral to tetrahedral, and then stellated it thirteen times.  This stellated polyhedron has pyritohedral symmetry, but this is easier … Continue reading

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A Chiral Polyhedron Made of Kites and Triangles, Along with Its Dual, Made of Triangles and Isosceles Trapezoids

To make this polyhedron using Stella 4d (available here), one starts with the icosahedron, drops the symmetry of the model down from icosahedral to tetrahedral, and then stellates it once. The result is a chiral solid featuring four triangular faces … Continue reading

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A Second Type of Double Icosahedron, and Related Polyhedra

After seeing my post about what I called the “double icosahedron,” which is two complete icosahedra joined at one common triangular face, my friend Tom Ruen brought my attention to a similar figure he likes. This second type of double icosahedron … Continue reading

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Augmenting, and Then Reaugmenting, the Icosahedron, with Icosahedra

A reader of this blog, in a comment on the last post here, asked what would happen if each face of an icosahedron were augmented by another icosahedron. I was also asked what the convex hull of such an icosahedron-cluster … Continue reading

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The Double Icosahedron, and Some of Its “Relatives”

The double icosahedron is simply an icosahedron, augmented on a single face by a second icosahedron. I thought it might be interesting to explore some transformations of this solid, using Stella 4d: Polyhedron Navigator (available here), and I was not … Continue reading

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Two Excellent Mathematical Websites

I usually only post my own work here, but today I’m giving a shout-out to the websites of a German friend of mine named Tadeusz E. Doroziński. He made this snub polyhedron with 362 faces, which I’m posting here as … Continue reading

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