Two Polyhedral Compounds

Posted on 17 August 2014 by RobertLovesPi

The image above is a compound of the rhombic triacontahedron (the dual of the icosidodecahedron) and a strombic hexacontahedron (the dual of the rhombicosidodecahedron). Below, you’ll find a compound of six square-based pyramids, all with their “centers of mass” (assuming uniform density) displaced, from the compound’s center, by equal amounts. In response to a request I have received, polyhedral images which rotate more slowly are coming soon . . . after I have finished posting my backlog of already-produced polyhedral .gif files, since there is no way to slow them down after they are already created.

The program I use for these polyhedral investigations is Stella 4d, available at www.software3d.com/Stella.php.

A Polyhedral Shuttlecraft, Adrift in Outer Space

Posted on 17 August 2014 by RobertLovesPi

Most of the polyhedra I post here have one of the symmetry-types which are collectively called “polyhedral” symmetry: tetrahedral, cuboctahedral, icosidodecahedral, or chiral variants of these. For a polyhedral representations of something like a shuttlecraft from Star Trek, though, such as this one, these symmetry-types must be abandoned.

Image credit: I made this using Stella 4d, available at www.software3d.com/Stella.php.

A Polyhedral Boomerang, in Flight

Posted on 17 August 2014 by RobertLovesPi

Most of the polyhedra I post here have one of the symmetry-types which are collectively called “polyhedral” symmetry: tetrahedral, cuboctahedral, icosidodecahedral, or chiral variants of these. For polyhedral representations of most real-world objects, though, such as this one, these symmetry-types must be abandoned.

Image credit: I made this using Stella 4d, available at www.software3d.com/Stella.php.

A Collection of Rotating Polyhedra with Cuboctahedral Symmetry

Posted on 17 August 2014 by RobertLovesPi

I have received a request to slow down the rotational speed of the polyhedral models I make and post here, and am going to try to do exactly that. First, though, I need to empty my collection of already-made image files which haven’t yet been posted, so that I can start again, with models which rotate more slowly, after deleting all the “speedy” ones. From my backlog of polyhedral images to post, then, here are some which have cuboctahedral symmetry.

This last one actually has the symmetry of a snub cube — a chiral variant of “normal” cuboctahedral symmetry.

All these images were created using Stella 4d: Polyhedron Navigator. If you’d like to try this program for yourself, the website to visit for a free trial download is www.software3d.com/Stella.php.

A Collection of Rotating Polyhedra with Icosidodecahedral Symmetry

Posted on 17 August 2014 by RobertLovesPi

I’ve received a request to slow down the rotational speed of the polyhedral models I make and post here, and am going to try to do exactly that. First, though, I need to empty my collection of already-made image files which haven’t yet been posted, so that I can start again, with models which rotate more slowly, after deleting all the “speedy” ones. From my backlog of polyhedral images to post, then, here are most of the ones with icosidodecahedral symmetry.

The next one shown has 362 faces — the closest I have come, so far, to a polyhedron with a number of faces which matches the number of days in a year.

The next one is a variant of the rhombic enneacontahedron, with that polyhedron’s wide rhombic faces replaced by kites, and its narrow rhombi replaced by pairs of isosceles triangles.

I call this next one a “thrice-truncated rhombic triacontahedron.”

In the remaining polyhedral images in this post, some faces have been rendered invisible. I do this, on occasion, either so that the front and back of the polyhedra can be seen at the same time, or simply for aesthetic reasons.

All of these images were created using Stella 4d: Polyhedron Navigator. If you’d like to try this program for yourself, the website to visit for a free trial download is www.software3d.com/Stella.php.