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 The Double Icosahedron, and Some of Its “Relatives”
 Two Excellent Mathematical Websites
 The Compound of the Octahedron and the Small Stellated Dodecahedron
 A Zoo of Zonohedra
 Seven Different Facetings of the Truncated Icosahedron
 Four Symmetrohedra
 Some TenPart Polyhedral Compounds
 Augmenting the Dodecahedron with Great Dodecahedra
 Using Rhombic Triacontahedra to Build an Icosidodecahedron
 Augmenting the Icosahedron with Great Icosahedra
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Monthly Archives: June 2018
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
Posted in Mathematics
Tagged double, geometry, icosahedron, Mathematics, polyhedra, polyhedron
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Two Excellent Mathematical Websites
I usually only post my own work here, but today I’m giving a shoutout 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
Posted in Blogging, Mathematics
Tagged blog, Blogging, Dorozinski, geometry, Mathematics, polyhedra, polyhedron, recommendation, recommended, Tadeusz, website
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The Compound of the Octahedron and the Small Stellated Dodecahedron
I made this rotating virtual model using Stella 4d: Polyhedron Navigator, which you can try for yourself at http://www.software3d.com/Stella.php. This solid is different from most twopart polyhedral compounds because an unusually high fraction of one polyhedron, the yellow octahedron, is … Continue reading
Posted in Mathematics
Tagged compound, geometry, Mathematics, octahedron, polyhedra, polyhedral, polyhedron, small stellated dodecahedron
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A Zoo of Zonohedra
Zonohedra are a subset of polyhedra with all faces in pairs of parallel and congruent zonogons. Zonogons are polygons with sides which occur only as parallel and congruent pairs of line segments. As a consequence of this, the faces of … Continue reading
Posted in Mathematics
Tagged geometry, Mathematics, polyhedra, polyhedron, zonohedra, zonohedron
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Seven Different Facetings of the Truncated Icosahedron
The polyhedron above is the truncated icosahedron, widely known as the pattern for most soccer balls. In the image below, the faces and edges have been hidden, leaving only the vertices. To make a faceted version of this polyhedron, these … Continue reading
Posted in Mathematics
Tagged facet, faceted, faceting, geometry, Mathematics, polyhedra, polyhedron, truncated icosahedra, truncated icosahedron
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Four Symmetrohedra
Symmetrohedra are polyhedra with some form of polyhedral symmetry, all faces convex, and many (but not all) faces regular. Here are four I have found using Stella 4d, a polyhedronmanipulation program you can try for yourself at http://www.software3d.com/Stella.php. The second … Continue reading
Posted in Mathematics
Tagged geometry, Mathematics, polyhedra, polyhedron, symmetrohedra, symmetrohedron
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Some TenPart Polyhedral Compounds
While examining different facetings of the dodecahedron, I stumbled across one which is also a compound of ten elongated octahedra. Here’s what this compound looks like with the edges and vertices hidden: Next, I’ll put the edges and vertices back, … Continue reading
Posted in Mathematics
Tagged compound, cube, geometry, Mathematics, octahedra, octahedron, polyhedra, polyhedral, polyhedron
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