Tag Archives: icosahedra

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

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An Icosahedron, Constructed from Smaller Polyhedra

The polyhedra at the vertices are rhombic triacontahedra, and the yellow edges are elongated rhombic prisms. This was made using Stella 4d, software you may try for free at this website.

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The Final Stellation of the Compound of Five Icosahedra

This was made using Stella 4d, software available at http://www.software3d.com/Stella.php.

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A Rhombic Ring of Icosahedra, Leading to a Rhombic Dodecahedron Made of Icosahedra

As it turns out, eight icosahedra form this rhombic ring, by augmentation: Measured from the centers of these icosahedra, the long and short diagonal of this rhombus are in a (√2):1 ratio. How do I know this? Because that’s the … Continue reading

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A Rhombic Dodecahedral Lattice, Made of Icosahedra

I used Stella 4d: Polyhedron Navigator to make this. You can find this program at http://www.software3d.com/Stella.php.

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Three Polyhedral Clusters of Icosahedra

In the last post on this blog, there were three images, and the first of these was a rotating icosahedron, rendered in three face-colors. After making it, I decided to see what I could build, using these tri-colored icosahedra as … Continue reading

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On Icosahedra, and Pyritohedral Symmetry

In this icosahedron, the four blue faces are positioned in such a way as to demonstrate tetrahedral symmetry. The same is true of the four red faces. The remaining twelve faces demonstrate pyritohedral symmetry, which is much less well-known. It … Continue reading

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