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.

A Tetrahedral Array of Pulsating Tetrahedra

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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

Tetrahedron with four pyramidal hats

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

Excavated Icosidodecahedron

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.

Excavated Icosidodecahedron dual

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

Compound of Augmented Dodeca and Augmented Icosa

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:

Compound of Augmented Dodeca and Augmented Icosa

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

Tetrakishexa stellation

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.

compound of eight off-center pyramids

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

compound of three short square dipyramids

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

more from the stellation series of the tetrakis cube

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

bizarre two-part compound

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

Two Polyhedral Compounds

Compound of the RTC and a strombic hexacontahedron

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.

Compound of Twelve Square-based pyramids

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