The Dodecahedron / Octahedron Compound

Posted on 12 September 2014 by RobertLovesPi

This rotating image was assembled using Stella 4d, available at http://www.software3d.com/Stella.php.

A Collection of Four Polyhedra Decorated with Mandalas

Posted on 11 September 2014 by RobertLovesPi

First, a cuboctahedron.

Next, its dual, the rhombic dodecahedron.

And, after that, the icosidodecahedron.

And finally, its dual, the rhombic triacontahedron.

All of these rotating images were assembled using Stella 4d, available at http://www.software3d.com/Stella.php.

Two Views of a Mandala with Fivefold Symmetry

Posted on 11 September 2014 by RobertLovesPi

Two Colorings of a Hollow Stella Octangula

Posted on 11 September 2014 by RobertLovesPi

Both of these versions of the stella octangula, or compound of two tetrahedra, were made with Stella 4d, software available at http://www.software3d.com/Stella.php.

A Polyhedral Caltrop

Posted on 11 September 2014 by RobertLovesPi

Created using Stella 4d, available at http://www.software3d.com/Stella.php.

A Great Dodecahedron, Augmented with Twelve Icosidodecahedra, and Its Dual

Posted on 11 September 2014 by RobertLovesPi

Each face of a great dodecahedron is a regular pentagon, and each of those pentagonal faces has an icosidodecahedron attached to it, in the figure above. The dual of this figure appears below.

Both images were created with Stella 4d, software available at www.software3d.com/Stella.php.

“I would accept that as an axiom.” ~Spock

Posted on 30 August 2014 by RobertLovesPi

I would also accept this as an axiom. It’s obviously true, but I see no way to prove it. It is not what Spock was referencing in the above quotation, but the content of the quote still applies.

Amazingly, though, I have encountered people who think this is up for debate.

It isn’t.

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.