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Rectified tesseract
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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.
Rectified tesseract | ||
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![]() Schlegel diagram Centered on cuboctahedron tetrahedral cells shown | ||
Type | Uniform 4-polytope | |
Schläfli symbol | r{4,3,3} = 2r{3,31,1} h3{4,3,3} | |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
Cells | 24 | 8 (3.4.3.4)![]() 16 (3.3.3) ![]() |
Faces | 88 | 64 {3} 24 {4} |
Edges | 96 | |
Vertices | 32 | |
Vertex figure | ![]() ![]() (Elongated equilateral-triangular prism) | |
Symmetry group | B4 [3,3,4], order 384 D4 [31,1,1], order 192 | |
Properties | convex, edge-transitive | |
Uniform index | 10 11 12 |
![](http://upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Rectified_tesseract_net.png/640px-Rectified_tesseract_net.png)
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.