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# Tag Archives: augmentation

## 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
1 Comment

## On Polyhedral Augmentation and Excavation

I have made many posts here using polyhedral augmentation, but what I haven’t done — yet — is explain it. I have also neglected the reciprocal function of augmentation, which is called excavation. It is now time to fix both … Continue reading

Posted in Mathematics
Tagged augmentation, cluster, excavation, geometry, icosahedron, icosidodecahedron, Mathematics, polyhedra, polyhedral, polyhedron, reciprocal, solid
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## The Compound of Five Cubes, Augmented with Thirty Snub Cubes: Three Versions

This cluster-polyhedron was made with Stella 4d, software you can try at this website. Above, it is colored by face-type, 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 coloring-schemes, 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
1 Comment

## A Polyhedral Investigation, Starting with an Augmentation of the Truncated Octahedron

If one starts with a central truncated octahedron, leaves its six square faces untouched, and augments its eight hexagonal faces with trianglular cupolae, this is the result. Seeing this, I did a quick check of its dual, and found it … Continue reading

Posted in Mathematics
Tagged augment, augmentation, convex hull, cupola, dual, truncated octahedron
2 Comments