| Rectified 5-simplex Rectified hexateron (rix) |
||
|---|---|---|
A5 Coxeter plane projection symmetry |
||
| Type | uniform polyteron | |
| Schläfli symbol | t1{34} | |
| Coxeter-Dynkin diagram | ||
| 4-faces | 12 | 6 {3,3,3} 6 t1{3,3,3} |
| Cells | 45 | 15 {3,3} 30 t1{3,3} |
| Faces | 80 | 80 {3} |
| Edges | 60 | |
| Vertices | 15 | |
| Vertex figure | {}x{3,3} |
|
| Coxeter group | A5, order 720 | |
| Base point | (0,0,0,0,1,1) | |
| Circumradius | 0.645497 | |
| Properties | convex, isogonal isotoxal | |
In five dimensional geometry, a rectified 5-simplex, is a uniform 5-polytope with 15 vertices, 60 edges, 80 triangular faces, 45 cells (15 tetrahedral, and 30 octahedral), and 12 4-faces (6 5-cell and 6 rectified 5-cells). It is also called 03,1 for its branching Coxeter-Dynkin diagram, shown as .
The rectified 5-simplex, 031, is second in a dimensional series of uniform polytopes, expressed by Coxeter as 13k series. The fifth figure is a Euclidean honeycomb, 331, and the final is a noncompact hyperbolic honeycomb, 431. Each progressive uniform polytope is constructed from the previous as its vertex figure.
| n | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|
| Coxeter group |
A3×A1 | A5 | D6 | E7 | = E7+ | E7++ |
| Coxeter diagram |
||||||
| Symmetry (order) |
(48) |
(720) |
(23,040) |
(2,903,040) |
(∞) |
(∞) |
| Graph | ∞ | ∞ | ||||
| Name | −131 | 031 | 131 | 231 | 331 | 431 |
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