Truncated tesseract

In geometry, a truncated tesseract is a uniform polychoron (4-dimensional uniform polytope) which is bounded by 24 cells: 8 truncated cubes, and 16 tetrahedra.

Construction

The truncated tesseract may be constructed by truncating the vertices of the tesseract at $1/(sqrt\{2\}+2)$ of the edge length. A regular tetrahedron is formed at each truncated vertex.

Projections

In the truncated cube first parallel projection of the truncated tesseract into 3-dimensional space, the image is laid out as follows:

* The projection envelope is a cube.
* Two of the truncated cube cells project onto a truncated cube inscribed in the cubical envelope.
* The other 6 truncated cubes project onto the square faces of the envelope.
* The 8 tetrahedral volumes between the envelope and the triangular faces of the central truncated cube are the images of the 16 tetrahedra, a pair of cells to each image.

Images

ee also

* Tesseract
* Uniform polychoron

External links

* [http://members.aol.com/Polycell/section2.html 2. Convex uniform polychora based on the tesseract (8-cell) and hexadecachoron (16-cell)] - Model 13
* [http://www.software3d.com/Tat.php Paper model of truncated tesseract] created using nets generated by Stella4D software