Rectified 8-cell

Rectified 8-cell
Schlegel diagram Centered on cuboctahedron tetrahedral cells shown
Type	Uniform polychoron
Cells	8 (3.4.3.4) 16 (3.3.3)
Faces	64 {3} 24 {4}
Edges	96
Vertices	32
Vertex figure	2 (3.3.3) 3 (3.4.3.4) (Elongated equilateral-triangular prism)
Schläfli symbol	t₁{4,3,3} t_0,2{3^1,1,1}
Coxeter-Dynkin diagrams
Symmetry group	B₄ [3,3,4] D₄ [3^1,1,1]
Properties	convex

In geometry, the rectified tesseract, or rectified 8-cell is a uniform polychoron (4-dimensional polytope) bounded by 24 cells: 8 cuboctahedra, and 16 tetrahedra.

[edit] Construction

The rectified tesseract may be constructed from the tesseract by truncating its vertices at the midpoints of its edges.

Wireframe

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

The projection envelope is a cube.
A cuboctahedron is inscribed in this cube, with its vertices lying at the midpoint of the cube's edges. The cuboctahedron is the image of two of the cuboctahedral cells.
The remaining 6 cuboctahedral cells are projected to the square faces of the cube.
The 8 tetrahedral volumes lying at the triangular faces of the central cuboctahedron are the images of the 16 tetrahedral cells, two cells to each image.