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Tag Archives: augment
Augmenting, and Then Reaugmenting, the Icosahedron, with Icosahedra
A reader of this blog, in a comment on the last post here, asked what would happen if each face of an icosahedron were augmented by another icosahedron. I was also asked what the convex hull of such an icosahedroncluster … Continue reading
Posted in Mathematics
Tagged augment, augmentation, augmented, cluster, geometry, icosahedron, Mathematics, polyhedra, polyhedral, polyhedron
6 Comments
Augmenting the Dodecahedron with Great Dodecahedra
These two polyhedra are the dodecahedron (left), and the great dodecahedron (right). Since the faces of both of these polyhedra are regular pentagons, it is possible to augment each of the dodecahedron’s twelve faces with a great dodecahedron. Here is … Continue reading
Posted in Mathematics
Tagged augment, augmentation, augmented, dodecahedra, dodecahedron, geometry, great, Mathematics, polyhedra, polyhedron
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Augmenting the Icosahedron with Great Icosahedra
These two polyhedra are the icosahedron (left), and the great icosahedron (right). Since the faces of both of these polyhedra are equilateral triangles, it is possible to augment each of the icosahedron’s twenty faces with a great icosahedron. Here … Continue reading
Posted in Mathematics
Tagged augment, augmentation, augmented, geometry, great, icosahedra, isocahedron, Mathematics, polyhedra, polyhedron
1 Comment
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 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 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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