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 A Second Type of Double Icosahedron, and Related Polyhedra
 Augmenting, and Then Reaugmenting, the Icosahedron, with Icosahedra
 The Double Icosahedron, and Some of Its “Relatives”
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 The Compound of the Octahedron and the Small Stellated Dodecahedron
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Tag Archives: augmented
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 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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