Rectified tesseract
From Wikipedia, the free encyclopedia
| Rectified tesseract | |
|---|---|
| (No image) | |
| 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) |
| Symmetry group | A4, [3,3,4] |
| Schläfli symbol | t1{4,3,3} |
| Properties | convex |
In geometry, the rectified tesseract is a uniform polychoron (4-dimensional polytope) bounded by 24 cells: 8 cuboctahedra, and 16 tetrahedra.
Contents |
[edit] Alternative names
- Rectified tesseract (Norman W. Johnson)
- Rit (Jonathan Bowers: for rectified tesseract)
- Rectified [four-dimensional] hypercube
- Rectified 8-cell
- Rectified octachoron
- Rectified [four-dimensional] measure polytope
- Rectified [four-dimensional regular] orthotope
- Runcic tesseract (Norman W. Johnson)
- Runcic [four-dimensional] hypercube
- Runcic 8-cell
- Runcic octachoron
- Runcic [four-dimensional] measure polytope
- Runcic [four-dimensional regular] orthotope
- Ambotesseract (Neil Sloane & John Horton Conway)
[edit] Construction
The rectified tesseract may be constructed from the tesseract by truncating its vertices at the midpoints of its edges.
[edit] 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.
