20-Thex: A Four-Dimensional Polytope


The 20-Thex:  A Four-Dimensional Polytope

In hyperspace, or four-space, there are six regular polychora, analogous to the Platonic Solids in three-space. Beyond the Platonics in the study of polyhedra comes, of course, the Archimedean Solids, which include many truncated forms of Platonic polyhedra.

In hyperspace, there are varieties of progressively-less regular polychora, also, and one of these, in a group called the truncates, is called 20-thex, or simply the “thex.” (Those are short names for this polychoron; it’s also called the truncated hexadecachoron, or truncated 16-cell.) What you see above is a (seemingly) three-dimensional projection of a thex, as it rotates in hyperspace.

Just as polyhedra have polygons as faces, polychora have polyhedra as unit cells. This is the net for the thex. As you can see, the thex is composed of both truncated tetrahedra and octahedra.


Both of these images were created using Stella 4d, which you can try for yourself at http://www.software3d.com/Stella.php.

Rotating Compound of the Tesseract and Its Dual


Rotating Compound of the Tesseract and Its Dual

Blue figure: a projection of the tesseract, or hypercube; also known as the 8-cell or octachoron — a four-dimensional figure composed of eight cubic cells in a regular arrangement.

Red figure: its dual, the 16-cell or hexadecachoron, which is composed of sixteen tetrahedral cells.

To buy (or just try) the software used to make this image, Stella 4d, please visit http://www.software3d.com/Stella.php.