The Greatly Augmented Icosidodecahedron, and Its Dual

Posted on 19 April 2015 by RobertLovesPi

If a central polyhedron’s pentagonal and triangular faces are augmented by great dodecahedra and great 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.

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

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.

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

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

The Greatly Augmented Rhombicosidodecahedron

Posted on 19 April 2015 by RobertLovesPi

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

A Fashionable Tetrahedron

Posted on 19 April 2015 by RobertLovesPi

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.

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

Posted on 18 April 2015 by RobertLovesPi

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.

Spinning Violet

Posted on 17 April 2015 by RobertLovesPi

Created using Stella 4d, available here.

Faceted Snub Dodecahedron

Posted on 17 April 2015 by RobertLovesPi

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.

Faceted Rhombcuboctahedron

Posted on 17 April 2015 by RobertLovesPi

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

Non-Convex and Cuboctahedral

Posted on 15 April 2015 by RobertLovesPi

Created with Stella 4d, available here.

A Stellated Polyhedron, Mostly Blue

Posted on 14 April 2015 by RobertLovesPi

This is the first stellation of the second polyhedron seen in the post just before this one, but with the color-scheme changed, on the grounds that I like blue. If you’d like to know more about how this polyhedron was created, I refer you to that post. Stella 4d was used to make these: software you can try right here.

The Pyramid-Excavated Icosidodecahedron, and Its Interesting Dual

Posted on 14 April 2015 by RobertLovesPi

To make this, I used the excavation-function of Stella 4d, set to remove pyramids with equal edge length from each face of an icosidodecahedron. You can try this program here.

The dual of this polyhedron is shown below.