The Greatly Augmented Icosidodecahedron, and Its Dual

Augmented Icosidodeca

If a central polyhedron’s pentagonal and triangular faces are augmented by great dodecahedra and icosahedra, I refer to it as a “greatly augmented” polyhedron. Here, this has been done with an icosidodecahedron. The same figure appears below, but in “rainbow color” mode.

Augmented Icosidodeca colored rainbow

In the next image, “color by face type,” based on symmetry, was used.

Augmented Icosidodeca colored by face type

The next image shows the dual of this polyhedral cluster, with face color chosen on the basis of number of sides.

Augmented Icosidodeca colored by whether sides have 5 or 16 sides

Here is another version of the dual, this one in “rainbow color” mode.

Augmented Icosidodeca colored rainbow DUAL

Finally, this image of the dual is colored based on face type.

Augmented Icosidodeca colored by face type DUAL

These six images were made with Stella 4d, which may be foundĀ here.

Posted in Mathematics | Tagged , , , , , , , , , , | 1 Comment

The Greatly Augmented Rhombicosidodecahedron

Greatly Augmented Rhombicosidodeca

I call this variant on the rhombicosidocahedron “greatly augmented” because it was formed by augmenting each pentagonal face of a central rhombicosidodecahedron with great dodecahedra, while each triangular face is augmented with great icosahedra. It was made using Stella 4d, which may be found here.

Posted in Mathematics | Tagged , , , , , , , , , , | 1 Comment

A Fashionable Tetrahedron

Tetrahedron with four pyramidal hats

You can tell this is a fashionable tetrahedron because he’s wearing four pyramidal hats — one to cover each vertex.

This bit of polyhedral silliness was created with Stella 4d, software you may try for free right here.

Posted in Mathematics | Tagged , , , , , , , , | 1 Comment

Two Polyhedral Compounds: the Dodecahedron / Truncated Octahedron, and Its Dual, the Icosahedron / Tetrakis Cube

Compound of Trunc Octa and Dodeca

That’s the compound of the dodecahedron and the truncated octahedron above. Shown next is its dual, the compound of the icosahedron and the tetrakis cube. Both compounds were made using Stella 4d: Polyhedron Navigator, which you may try here.

Compound of tetrakis cube and icosa

Posted in Mathematics | Tagged , , , , , , , , , | Leave a comment

Spinning Violet

spinning violet

Created using Stella 4d, available here.

Posted in Art, Mathematics | Tagged , , , , , , , | Leave a comment

Faceted Snub Dodecahedron

Faceted Snub Dodeca

Facetings are created by joining vertices to other vertices, but not choosing the vertices in the usual manner, which results in new positions for edges and faces. Faceting is also the reciprocal-function for polyhedral stellation. This is one of many possible facetings of the snub dodecahedron, and I created it using Stella 4d, which you can find here.

Posted in Mathematics | Tagged , , , , , | 3 Comments

Faceted Rhombcuboctahedron

faceted rhombcuboctahedron

This faceting was created using Stella 4d, available here.

Posted in Mathematics | Tagged , , , , , , | 1 Comment