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A Compound of a Slightly-Truncated Icosahedron and the Rhombic Triacontahedron
41 Dodecahedra
Stellar Array
A great dodecahedron (red) sits in the middle of this polyhedral cluster. The polyhedra touching the one in the center are blue small stellated dodecahedra. Finally, there are yellow great stellated dodecahedra on the outside.
I assembled this polyhedral cluster using Stella 4d, which you can try for yourself at http://www.software3d.com/Stella.php.
Posted in Mathematics
Tagged dodecahedra, dodecahedron, geometry, great, Mathematics, polyhedra, polyhehdron, small, stellated
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The Eleventh Stellation of the Truncated Octahedron Is an Interesting Polyhedral Compound
This compound has three parts: two tetrahedra, plus one smaller cube. I made it using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.
Posted in Mathematics
Tagged compound, cube, geometry, Mathematics, polyhedra, polyhedral, polyhedron, stellated, stellation, tetrahedra, tetrahedron, truncated octahedra
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A Symmetrohedron
Symmetrohedra are symmetrical polyhedra which have many, but not all, faces regular. I just found one which has square faces, regular hexagons, regular octagons, and a bunch of scalene triangles as the irregular faces.
To form this polyhedron, I started with the great rhombcuboctahedron, then formed its base/dual compound. I then took the convex hull of this compound, and then formed the dual of that convex hull, producing the polyhedron you see above. All of this was done using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.
Posted in Mathematics
Tagged geometry, Mathematics, polyhedra, polyhedron, symmetrohedra, symmetrohedron
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