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Tag Archives: cluster
An Icosahedron Augmented with Twenty Great Icosahedra, together with the Dual of this ClusterPolyhedron
The clusterpolyhedron above was formed by augmenting a central isocahedron with twenty great icosahedra. The dual of this cluster is shown below. Both these images were created using Stella 4d, which you may try for free at http://www.software3d.com/Stella.php.
Posted in Mathematics
Tagged cluster, geometry, great icosahedron, icosahedron, Mathematics, polyhedra, polyhedron
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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
Cluster of Six Rhombicosidodecahedra
To make this cluster, start with a cuboctahedron, then augment each of its square faces with rhombicosidodecahedra. Although the cuboctahedron has cuboctahedral symmetry, this cluster does not — rather, it has tetrahedral symmetry. I created this using Stella 4d, which … Continue reading
Posted in Mathematics
Tagged cluster, geometry, Mathematics, polyhedra, polyhedral, polyhedron, rhombicosidodecahedra, rhombicosidodecahedron
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A Dozen Snub Dodecahedra, Surrounding a Dodecahedral Core
Software used — Stella 4d: Polyhedral Navigator, available as a free trial download at http://www.software3d.com/Stella.php.
Posted in Mathematics
Tagged cluster, geometry, Mathematics, polyhedra, polyhedral, polyhedron, snub dodecahedron
1 Comment
Three Views of a Rotating Cluster of 33 Icosidodecahedra
To make these three rotating clusterpolyhedra, I started with one icosidodecahedron in the center, then augmented each of its 32 faces with overlapping, additional icosidodecahedra, for a total of 33 icosidodecahedra per cluster. In the first image, only two colors are … Continue reading
Posted in Mathematics
Tagged cluster, geometry, icosidodecahedra, icosidodecahedral, icosidodecahedron, Mathematics, polyhedra, polyhedral, polyhedron
2 Comments
An Open Cluster of Polyhedra
From the center to the outside, this cluster contains one icosahedron, twenty octahedra, twenty icosidodecahedra, twenty more octahedra, and, finally, twenty rhombicosidodecahedra. All three of the images here were created using Stella 4d, a program you may try, free, at … Continue reading
Posted in Mathematics
Tagged cluster, geometry, Mathematics, polyhedra, polyhedral, polyhedron
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A Festive Cluster of Polyhedra
This is what you get if you start with an icosahedron, augment each of its faces with tetrahedra, and then augment the tetrahedral faces with octahedra. I made it using Stella 4d, a program you may try for free at … Continue reading
Posted in Art, Mathematics
Tagged Art, cluster, festive, geometric, geometrical, geometry, mathematical, Mathematics, polyhedra, polyhedral, polyhedron
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