In geometry, the rectified tesseract, rectified 8-cell is a uniform 4-polytope (4-dimensional polytope) bounded by 24 cells: 8 cuboctahedra, and 16 tetrahedra. It has half the vertices of a runcinated tesseract, with its construction, called a runcic tesseract. It has two uniform constructions, as a rectified 8-cell r{4,3,3} and a cantellated demitesseract, rr{3,31,1}, the second alternating with two types of tetrahedral cells. E. L. Elte identified it in 1912 as a semiregular polytope, labeling it as tC8.

Construction

The rectified tesseract may be constructed from the tesseract by truncating its vertices at the midpoints of its edges. The Cartesian coordinates of the vertices of the rectified tesseract with edge length 2 is given by all permutations of:

Images

Projections

In the cuboctahedron-first parallel projection of the rectified tesseract into 3-dimensional space, the image has the following layout:

Alternative names

Related uniform polytopes

Runcic cubic polytopes

Tesseract polytopes