Spectral Tetrahedra

Stella 4d: Polyhedron Navigator has a “put models on vertices” function which I used to build this complex of tetrahedra. If you’d like to try this software for yourself, there is a free trial version available at http://www.software3d.com/Stella.php.

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.

The Eleventh Stellation of the Truncated Octahedron Is an Interesting Polyhedral Compound

This compound has three parts: two tetrahedra, plus one smaller cube. I made it using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.

An Offspring of a Dodecahedron and a Tetrahedron

Dodeca tetrahedrally stellated mutliple times

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Stellated Dodeca rb

To make this polyhedron, I first changed the symmetry-type of a dodecahedron from icosahedral to tetrahedral, then stellated it twice. This was done using Stella 4d, a program you may try for free at http://www.software3d.com/Stella.php.

Three Polyhedra Which Resemble Caltrops

Caltrops, when resting on a horizontal surface, have a sharp, narrow point sticking straight up. Stepping on such objects is painful. Most polyhedra do not have such a shape; the most well-known example of an exception to this is the tetrahedron. This fact is well-known to many players of role-playing games, who often use the term “d4” for tetrahedral dice, and who usually try to avoid stepping on them. Here are some other polyhedra which resemble caltrops. All were made using Stella 4d, software available at this website. The first two images may be made larger by simply clicking on them.

The third example, made with the same program, varies this idea somewhat: in physical form, resting on a floor, this caltrop-polyhedron would have three, not just one, potentially foot-damaging “spikes” sticking straight up.

12-pointed caltrop

 

An Oblique Truncation of the Tetrahedron

kite-bounded tetrahedron

This polyhedron has sixteen faces: four equilateral triangles, and a dozen kites. It was created using Stella 4d, which may be found at http://www.software3d.com/Stella.php.

A Hybrid of the Tetrahedron and the Great Dodecahedron

I made this by stellating a dodecahedron repeatedly, but doing so with Stella 4d, the polyhedral-manipulation software I use (available here), set to use tetrahedral symmetry, rather than the higher-order icosahedral symmetry (which I often call “icosidodecahedral” symmetry) inherent to Platonic dodecahedra.

Hybrid of great Dodeca and the tet

The same polyhedron appears below, but with the coloring-scheme, rotational direction, and rotational speed all set differently.

Tetrahedron meets great dodecahedron