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# Tag Archives: augment

## 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

## 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 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

## A Cluster of Nine Octahedra, and Related Polyhedra

If one starts with a central octahedron, then augments each of its eight triangular faces with identical octahedra, this is the result. It is then possible to augment each visible triangle of this cluster with yet more octahedra, which produces … Continue reading

Posted in Mathematics
Tagged augment, augmentation, cluster, convex hull, geometry, Mathematics, octahedra, octahedron, polyhedra, polyhedral, polyhedron, stellate, stellation
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## An Experiment Involving Augmentation of Octahedra with More Octahedra, Etc.

I’m going to start this experiment with a single octahedron, with faces in two colors, placed so that two faces which share an edge are always of different colors. Next, I will augment the red faces — and only the … Continue reading

Posted in Mathematics
Tagged augment, augmentation, convex hull, dual, experiment, geometry, Mathematics, octahedron, otahedra, polyhedra, polyhedron, Stella, Stella 4d
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## A Polyhedral Journey, Beginning with Face-Based Zonohedrification of an Icosahedron

To begin this, I took an icosahedron, and made a zonish polyhedron with it, with the new faces based on the zones of the existing faces. Here’s the result. Next, I started stellating the polyhedron above. At the sixth stellation, … Continue reading

Posted in Mathematics
Tagged augment, augmentation, convex hull, geometry, icosahedron, Mathematics, polyhedra, polyhedral, polyhedron, stellate, stellation, zonish, zonohedrification, zonohedron
2 Comments

## A Simulation of Crystalline Growth Using Polyhedral Augmentation

Crystals and crystalline growth have been studied for centuries because of, at least in part, their symmetry. Crystals are cut in such a way as to increase this symmetry even more, because most people find symmetry attractive. However, where does … Continue reading

Posted in Mathematics, Science and Scientists
Tagged aesthetic, augment, augmentation, beauty, chemistry, cluster, crstalline, crystal, geometry, growth, Mathematics, polyhedra, polyhedral, polyhedron, rhombicosidodecahedron, science, symmetry, tetrahedron
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