I made this using *Stella 4d*, which you can try for free right here.

# Tag Archives: pyramid

# An Excavated Tetrahedron

Polyhedral excavation is the opposite of augmentation. In this excavated tetrahedron, short pyramids have been removed from each face. I made this using *Stella 4d*, which can be tried for free at this website.

# Five Tetrahedra

I made this variation of Kepler’s* Stella Octangula*, using *Stella 4d*, software you can try for free at this website.

# A Pyramid-Augmented Snub Dodecahedron

All of the edges of this polyhedron have the same length. I made it using *Stella 4d: Polyhedron Navigator*, which you can try for free at this website.

# A Tetrahedral Array of Pulsating Tetrahedra

I created this using *Stella 4d: Polyhedron Navigator*. You may try this software, for free, at http://www.software3d.com/Stella.php.

# A Fashionable Tetrahedron

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.

# The Pyramid-Excavated Icosidodecahedron, and Its Interesting Dual

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.

# The Compound of the Pyramid-Excavated Dodecahedron and Tetrahedrally-Excavated Icosahedron, Together with Its Interesting Dual

This is the familiar dodecahedron/icosahedron compound, but with each face of both components of the compound altered by the excavation of an equal-edge-length pyramid. To make it, as well as the rotating image below, I used *Stella 4d*, which you can find here.

Also, here is the dual of the compound above:

# More Polyhedra, Including Some Compounds, from the Stellation-Series of the Tetrakis Cube

The next one is a compound of eight off-center pyramids. By this point, I had gone so far into the stellation-series (a search I began when preparing the post before this one) that I had lost count.

This one is a compound of three short square-based dipyramids:

This one, according to *Stella 4d*, is a compound of three parts, but I can’t quite figure out what the parts are!

Here is another “mystery compound,” this one with two parts:

*Stella 4d*, which I used to make these, may be tried here.

# Two Polyhedral Compounds

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.