Rectified tesseract explained

bgcolor=#e7dcc3 align=center colspan=3Rectified tesseract
bgcolor=#ffffff align=center colspan=3
Schlegel diagram
Centered on cuboctahedron
tetrahedral cells shown
TypeUniform 4-polytope
Schläfli symbolr =

\left\{\begin{array}{l}4\\3,3\end{array}\right\}


2r
h3
Coxeter-Dynkin diagrams

=
Cells248 (3.4.3.4)
16 (3.3.3)
Faces8864
24
Edges96
Vertices32
Vertex figure
(Elongated equilateral-triangular prism)
Symmetry groupB4 [3,3,4], order 384
D4 [3<sup>1,1,1</sup>], order 192
Propertiesconvex, edge-transitive
Uniform index10 11 12
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 and a cantellated demitesseract, rr, 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:

(0,\pm\sqrt{2},\pm\sqrt{2},\pm\sqrt{2})

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

Tesseract polytopes

References