| Correct 9-simplex |
|---|
 |
| Type of | The correct nine-dimensional politop |
| Shlefly symbol | {3,3,3,3,3,3,3,3} |
| 8-dimensional cells | 10 |
| 7-dimensional cells | 45 |
| 6-dimensional cells | 120 |
| 5 dimensional cells | 210 |
| 4-dimensional cells | 252 |
| Cells | 210 |
| Facets | 120 |
| Riber | 45 |
| Top | 10 |
| Vertex figure | The correct 8-simplex |
| Dual politop | He is ( self-dual ) |
The correct 9-simplex , or decaiotton , or deca-9-top is the correct self - dual nine - dimensional polytope . It has 10 vertices, 45 edges, 120 faces having the shape of a regular triangle, 210 regular tetrahedral cells, 252 five -cell 4-cells, 210 5-cells having the shape of a regular 5-simplex , 120 6-cells having the shape of a regular 6-simplex , 45 7 cells having the shape of a regular 7-simplex and 10 8 cells having the shape of a regular 8-simplex . Its dihedral angle is equal to arccos (1/9) , i.e. approximately 83.62 °.
The correct 9-sipmlex can be placed in the Cartesian coordinate system as follows (the length of the body edge is 2 and the center is at the origin):
- {\ displaystyle \ left ({\ sqrt {1/45}}, \ 1/6, \ {\ sqrt {1/28}}, \ {\ sqrt {1/21}}, \ {\ sqrt {1 / 15}}, \ {\ sqrt {1/10}}, \ {\ sqrt {1/6}}, \ {\ sqrt {1/3}}, \ \ pm 1 \ right)}
- {\ displaystyle \ left ({\ sqrt {1/45}}, \ 1/6, \ {\ sqrt {1/28}}, \ {\ sqrt {1/21}}, \ {\ sqrt {1 / 15}}, \ {\ sqrt {1/10}}, \ {\ sqrt {1/6}}, \ -2 {\ sqrt {1/3}}, \ 0 \ right)}
- {\ displaystyle \ left ({\ sqrt {1/45}}, \ 1/6, \ {\ sqrt {1/28}}, \ {\ sqrt {1/21}}, \ {\ sqrt {1 / 15}}, \ {\ sqrt {1/10}}, \ - {\ sqrt {3/2}}, \ 0, \ 0 \ right)}
- {\ displaystyle \ left ({\ sqrt {1/45}}, \ 1/6, \ {\ sqrt {1/28}}, \ {\ sqrt {1/21}}, \ {\ sqrt {1 / 15}}, \ -2 {\ sqrt {2/5}}, \ 0, \ 0, \ 0 \ right)}
- {\ displaystyle \ left ({\ sqrt {1/45}}, \ 1/6, \ {\ sqrt {1/28}}, \ {\ sqrt {1/21}}, \ - {\ sqrt {5 / 3}}, \ 0, \ 0, \ 0, \ 0 \ right)}
- {\ displaystyle \ left ({\ sqrt {1/45}}, \ 1/6, \ {\ sqrt {1/28}}, \ - {\ sqrt {12/7}}, \ 0, \ 0, \ 0, \ 0, \ 0 \ right)}
- {\ displaystyle \ left ({\ sqrt {1/45}}, \ 1/6, \ - {\ sqrt {7/4}}, \ 0, \ 0, \ 0, \ 0, \ 0, \ 0 \ right)}
- {\ displaystyle \ left ({\ sqrt {1/45}}, \ -4/3, \ 0, \ 0, \ 0, \ 0, \ 0, \ 0, \ 0 \ right)}
- {\ displaystyle \ left (-3 {\ sqrt {1/5}}, \ 0, \ 0, \ 0, \ 0, \ 0, \ 0, \ 0, \ 0 \ right)}
