A Large Collection of Polyhedra with Icosidodecahedral Symmetry, Some of Them Chiral

Posted on 8 May 2015 by RobertLovesPi

I made these using Stella 4d, available here.

A Dodecahedron with Four Symetrically-Truncated Vertices

Posted on 8 May 2015 by RobertLovesPi

Dodecahedra have icosahedral (also called icosidodecahedral) symmetry. In the figure above, this symmetry is changed to tetrahedral, by truncation of four vertices with positions corresponding to the vertices (or, instead, faces) of a tetrahedron. The interchangeability of vertices and faces for the tetrahedron is related to the fact that the tetrahedron is self-dual.

[Image created using Stella 4d, available here.]

Symmetrically Shattering Glass

Posted on 7 May 2015 by RobertLovesPi

Created with Stella 4d, available here.

Four Vases

Posted on 6 May 2015 by RobertLovesPi

Created with Stella 4d, a program available here.

Selections from the Stellation-Series of the Icosidodecahedron

Posted on 4 May 2015 by RobertLovesPi

The icosidodecahedron has a long and interesting stellation-series, and you can see the whole thing using Stella 4d, the program I used to make the rotating .gifs here. Rather than keep the scale the same in each frame, I set the program to make the polyhedron as large as possible, while still fitting in the image-box. This creates the illusion that the polyhedra below are “breathing.”

The polyhedron above is the 20th stellation of the icosidodecahedron — the one that appeared as the sole image in the last post here, but with completely different colors. The next one shown is the 31st stellation.

The 55th stellation is immediately above, while the next one is the 69th.

The 84th stellation is immediately above, while the next one is the 89th.

The 106th stellation is immediately above, while the next one is the the 110th.

The 135th stellation is immediately above, while the next one, which is chiral, is the 157th.

Glimpses of the Invisible

Posted on 3 May 2015 by RobertLovesPi

Created using Stella 4d, available here, by multiple stellations of a black icosidodecahedron, rendered as a rotating figure, against a black background.

32 Octagonal Mandalas, Rotating in the Dark

Posted on 3 May 2015 by RobertLovesPi

To create the octagonal mandalas, I used Geometer’s Sketchpad and MS-Paint. I then projected them onto the faces of an all-but invisible icosidodecahedron, and created this rotating .gif image of it, using Stella 4d: Polyhedron Navigator, software you can try for free, right here.

A Dozen Octagonal Mandalas, Rotating in the Dark

Posted on 3 May 2015 by RobertLovesPi

To create the octagonal mandalas, I used Geometer’s Sketchpad and MS-Paint. I then projected them onto the faces of an all-but invisible dodecahedron, and created this rotating .gif image of it, using Stella 4d: Polyhedron Navigator, software you can try for free, right here.