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.
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.
I stumbled across this compound yesterday, an example of exploratory polyhedral manipulation using Stella 4d producing an unexpected result. If you would like to experiment with a free trial download of this program, before deciding whether or not to purchase the fully-functioning version, simply click here: www.software3d.com/Stella.php.
Music: the first two tracks from the Murder By Death album Like the Excorcist, But More Breakdancing. Please visit their website, http://www.murderbydeath.com, to buy this band’s music and merchandise. While you’re there, I recommend checking their concert calendar, to see if they may be playing near you soon. Murder By Death concerts, which I’ve seen six times now, are not to be missed!
Visuals: rotating polyhedra, all with icosidodecahedral symmetry, generated using Stella 4d: Polyhedron Navigator, which you can try for yourself at http://www.software3d.com/Stella.php. The polyhedra shown are, in order of appearance:
The icosahedron
The compound of the icosahedron and its dual, the dodecahedron
The dodecahedron, with all faces the same color
The small stellated dodecahedron, or first stellation of the dodecahedron, in a single color
The small stellated dodecahedron, with only parallel faces having the same color (six-color arrangement)
The great dodecahedron, or second stellation of the dodecahedron, six-color arrangement
The great stellated dodecahedron, or third stellation of the dodecahedron, six-color arrangement
Stellating the dodecahedron a fourth time, to return it to its original form, but in the six-color arrangement this time
The icosidodecahedron, with triangular faces invisible, and pentagonal faces shown using the six-color arrangement
The icosidodecahedron, all faces visible now, and colored by face type
The fourth stellation of the icosidodecahedron (its first stellation is the dodecahedron, the second is the icosahedron, and the third is the compound of the first two, all of which have already been seen)
The fifth stellation of the icosidodecahedron
The convex hull of the fifth stellation of the icosidodecahedron, which is a slightly-truncated icosahedron
The truncated icosahedron which is a true Archimedean Solid, since all its faces are regular
The truncated icosahedron’s second stellation (the first is the already-seen icosahedron)
Since I stumbled across this by stellating other polyhedra, I’ve never seen what a face of one component of this compound looks like, without having part of that face covered. My best guess is that the faces (of which there are eight in each part of the compound) are kites.
RobertLovesPi.net 