Rectified 8-cell

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.

Construction

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

Images

Projections

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.

Alternative names

*Rit (Jonathan Bowers: for rectified tesseract)
*Ambotesseract (Neil Sloane & John Horton Conway)
*Rectified tesseract (Norman W. Johnson)
*Rectified 4-hypercube
*Rectified 8-cell
*Rectified octachoron
*Rectified 4-measure polytope
*Rectified 4-regular orthotope
*Runcic tesseract (Norman W. Johnson)
*Runcic 4-hypercube
*Runcic 8-cell
*Runcic octachoron
*Runcic 4-measure polytope
*Runcic 4-regular orthotope

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 11