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Tag Archives: augmented
Augmenting the Octahedron with Octahedra, Repeatedly.
This is an octahedron. If you augment each face of an octahedron with more octahedra, you end up with this. One can then augment each triangular face of this with yet more octahedra. Here’s the next iteration: This could, of … Continue reading
Posted in Mathematics
Tagged augment, augmentation, augmented, geometry, Mathematics, octahedra, octahedron, polyehdral, polyhedra, polyhedron
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The Compound of Five Cubes, Augmented with Thirty Snub Cubes: Three Versions
This clusterpolyhedron was made with Stella 4d, software you can try at this website. Above, it is colored by facetype, referring to each face’s position within the overall cluster. In the image below, the original compound of five cubes contained … Continue reading
Posted in Mathematics
Tagged augment, augmentation, augmented, cluster, compound, cube, five, geometry, Mathematics, polyhedra, polyhedral, polyhedron, snub cube
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A Truncated Icosahedron, with Hexagons Augmented By Triangular Pyramids, in a Chiral Pattern
I made this using Stella 4d: Polyhedron Navigator, software available here.
Posted in Mathematics
Tagged augmentation, augmented, chiral, chirality, geometry, Mathematics, polyhedra, polyhedron, truncated icosahedron
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A Great Icosahedron, Augmented with Twenty Icosahedra
The polyhedral clusters above and below use different coloringschemes, but are otherwise identical. Invisible, in the center, is a great icosahedron. Each of its faces has been augmented by a (Platonic) icosahedron. Both images were created using Stella 4d, software … Continue reading
Posted in Mathematics
Tagged augmentation, augmented, geometry, great icosahedron, icosahedron, polyhedra, polyhedron
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The Greatly Augmented Rhombicosidodecahedron
I call this variant on the rhombicosidocahedron “greatly augmented” because it was formed by augmenting each pentagonal face of a central rhombicosidodecahedron with great dodecahedra, while each triangular face is augmented with great icosahedra. It was made using Stella 4d, … Continue reading
Posted in Mathematics
Tagged augmentation, augmented, geometry, great, great dodecahedron, great icosahedron, greatly, Mathematics, polyhedra, polyhedron, rhombicosidodecahedron
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Icosidodecahedra, Icosahedra, and Dodecahedra
If one starts with a single icosidodecahedron, and then augments its pentagonal faces with dodecahedra, and its trianguar faces with icosahedra, this is the result. This figure has gaps in it where two pentagons and two triangles meet around a … Continue reading
Posted in Mathematics
Tagged augmentation, augmented, cluster, dodecahedron, geometry, icosahedron, icosidodecahedron, Mathematics, polyhedra, polyhedral, polyhedron
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An Icosahedron, Augmented with Twenty Triangular Cupolae, Together with Its Dual
After making the above polyhedron using Stella 4d (a program you can try for free at http://www.software3d.com/Stella.php), I checked its dual, which is shown below. I was surprised at its appearance, for it resembles a stellated polyhedron, even though it … Continue reading
Posted in Mathematics
Tagged augmentation, augmented, cupola, cupolae, dual, geometry, icosahedron, Mathematics, polyhedra, polyhedron, triangular
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