Grup titik
Daftar grup titik > Eight dimensions

The following table gives the eight-dimensional reflection groups (excluding those that are lower-dimensional reflection groups), by listing them as Coxeter groups. Related chiral groups exist for each with half the order, defined by an even number of reflections, and can be represented by the bracket Coxeter notation with a '+' exponent, for example [3,3,3,3,3,3,3]+ has seven 3-fold gyration points and symmetry order 181440.
| Coxeter group | Coxeter group | Coxeter diagram | Order | Related polytopes |
| --- | --- | --- | --- | --- |
| A8 | [3,3,3,3,3,3,3] |  | 362880 (9!) | 8-simplex |
| A8×2 | [[3,3,3,3,3,3,3]] |  | 725760 (2×9!) | 8-simplex dual compound |
| BC8 | [4,3,3,3,3,3,3] |  | 10321920 (288!) | 8-cube,8-orthoplex |
| D8 | [3,3,3,3,3,31,1] |  | 5160960 (278!) | 8-demicube |
| E8 | [3,3,3,3,32,1] |  | 696729600 (192×10!) | 421, 241, 142 |
| A7×A1 | [3,3,3,3,3,3,2] |  | 80640 | 7-simplex prism |
| BC7×A1 | [4,3,3,3,3,3,2] |  | 645120 | 7-cube prism |
| D7×A1 | [3,3,3,3,31,1,2] |  | 322560 | 7-demicube prism |
| E7×A1 | [3,3,3,32,1,2] |  | 5806080 | 321 prism, 231 prism, 142 prism |
| A6×I2(p) | [3,3,3,3,3,2,p] |  | 10080p | duoprism |
| BC6×I2(p) | [4,3,3,3,3,2,p] |  | 92160p | duoprism |
| D6×I2(p) | [3,3,3,31,1,2,p] |  | 46080p | duoprism |
| E6×I2(p) | [3,3,32,1,2,p] |  | 103680p | duoprism |
| A6×A12 | [3,3,3,3,3,2,2] |  | 20160 | duoprism |
| BC6×A12 | [4,3,3,3,3,2,2] |  | 184320 | duoprism |
| D6×A12 | [33,1,1,2,2] |  | 92160 | duoprism |
| E6×A12 | [3,3,32,1,2,2] |  | 207360 | duoprism |
| A5×A3 | [3,3,3,3,2,3,3] |  | 17280 | duoprism |
| BC5×A3 | [4,3,3,3,2,3,3] |  | 92160 | duoprism |
| D5×A3 | [32,1,1,2,3,3] |  | 46080 | duoprism |
| A5×BC3 | [3,3,3,3,2,4,3] |  | 34560 | duoprism |
| BC5×BC3 | [4,3,3,3,2,4,3] |  | 184320 | duoprism |
| D5×BC3 | [32,1,1,2,4,3] |  | 92160 | duoprism |
| A5×H3 | [3,3,3,3,2,5,3] |  |  | duoprism |
| BC5×H3 | [4,3,3,3,2,5,3] |  |  | duoprism |
| D5×H3 | [32,1,1,2,5,3] |  |  | duoprism |
| A5×I2(p)×A1 | [3,3,3,3,2,p,2] |  |  | duoprism |
| BC5×I2(p)×A1 | [4,3,3,3,2,p,2] |  |  | duoprism |
| D5×I2(p)×A1 | [32,1,1,2,p,2] |  |  | duoprism |
| A5×A13 | [3,3,3,3,2,2,2] |  |  | duoprism |
| BC5×A13 | [4,3,3,3,2,2,2] |  |  | duoprism |
| D5×A13 | [32,1,1,2,2,2] |  |  | duoprism |
| A4×A4 | [3,3,3,2,3,3,3] |  |  | duoprism |
| BC4×A4 | [4,3,3,2,3,3,3] |  |  | duoprism |
| D4×A4 | [31,1,1,2,3,3,3] |  |  | duoprism |
| F4×A4 | [3,4,3,2,3,3,3] |  |  | duoprism |
| H4×A4 | [5,3,3,2,3,3,3] |  |  | duoprism |
| BC4×BC4 | [4,3,3,2,4,3,3] |  |  | duoprism |
| D4×BC4 | [31,1,1,2,4,3,3] |  |  | duoprism |
| F4×BC4 | [3,4,3,2,4,3,3] |  |  | duoprism |
| H4×BC4 | [5,3,3,2,4,3,3] |  |  | duoprism |
| D4×D4 | [31,1,1,2,31,1,1] |  |  | duoprism |
| F4×D4 | [3,4,3,2,31,1,1] |  |  | duoprism |
| H4×D4 | [5,3,3,2,31,1,1] |  |  | duoprism |
| F4×F4 | [3,4,3,2,3,4,3] |  |  | duoprism |
| H4×F4 | [5,3,3,2,3,4,3] |  |  | duoprism |
| H4×H4 | [5,3,3,2,5,3,3] |  |  | duoprism |
| A4×A3×A1 | [3,3,3,2,3,3,2] |  |  | duoprism prisms |
| A4×BC3×A1 | [3,3,3,2,4,3,2] |  |  | duoprism prisms |
| A4×H3×A1 | [3,3,3,2,5,3,2] |  |  | duoprism prisms |
| BC4×A3×A1 | [4,3,3,2,3,3,2] |  |  | duoprism prisms |
| BC4×BC3×A1 | [4,3,3,2,4,3,2] |  |  | duoprism prisms |
| BC4×H3×A1 | [4,3,3,2,5,3,2] |  |  | duoprism prisms |
| H4×A3×A1 | [5,3,3,2,3,3,2] |  |  | duoprism prisms |
| H4×BC3×A1 | [5,3,3,2,4,3,2] |  |  | duoprism prisms |
| H4×H3×A1 | [5,3,3,2,5,3,2] |  |  | duoprism prisms |
| F4×A3×A1 | [3,4,3,2,3,3,2] |  |  | duoprism prisms |
| F4×BC3×A1 | [3,4,3,2,4,3,2] |  |  | duoprism prisms |
| F4×H3×A1 | [3,4,2,3,5,3,2] |  |  | duoprism prisms |
| D4×A3×A1 | [31,1,1,2,3,3,2] |  |  | duoprism prisms |
| D4×BC3×A1 | [31,1,1,2,4,3,2] |  |  | duoprism prisms |
| D4×H3×A1 | [31,1,1,2,5,3,2] |  |  | duoprism prisms |
| A4×I2(p)×I2(q) | [3,3,3,2,p,2,q] |  |  | triaprism |
| BC4×I2(p)×I2(q) | [4,3,3,2,p,2,q] |  |  | triaprism |
| F4×I2(p)×I2(q) | [3,4,3,2,p,2,q] |  |  | triaprism |
| H4×I2(p)×I2(q) | [5,3,3,2,p,2,q] |  |  | triaprism |
| D4×I2(p)×I2(q) | [31,1,1,2,p,2,q] |  |  | triaprism |
| A4×I2(p)×A12 | [3,3,3,2,p,2,2] |  |  |  |
| BC4×I2(p)×A12 | [4,3,3,2,p,2,2] |  |  |  |
| F4×I2(p)×A12 | [3,4,3,2,p,2,2] |  |  |  |
| H4×I2(p)×A12 | [5,3,3,2,p,2,2] |  |  |  |
| D4×I2(p)×A12 | [31,1,1,2,p,2,2] |  |  |  |
| A4×A14 | [3,3,3,2,2,2,2] |  |  |  |
| BC4×A14 | [4,3,3,2,2,2,2] |  |  |  |
| F4×A14 | [3,4,3,2,2,2,2] |  |  |  |
| H4×A14 | [5,3,3,2,2,2,2] |  |  |  |
| D4×A14 | [31,1,1,2,2,2,2] |  |  |  |
| A3×A3×I2(p) | [3,3,2,3,3,2,p] |  |  |  |
| BC3×A3×I2(p) | [4,3,2,3,3,2,p] |  |  |  |
| H3×A3×I2(p) | [5,3,2,3,3,2,p] |  |  |  |
| BC3×BC3×I2(p) | [4,3,2,4,3,2,p] |  |  |  |
| H3×BC3×I2(p) | [5,3,2,4,3,2,p] |  |  |  |
| H3×H3×I2(p) | [5,3,2,5,3,2,p] |  |  |  |
| A3×A3×A12 | [3,3,2,3,3,2,2] |  |  |  |
| BC3×A3×A12 | [4,3,2,3,3,2,2] |  |  |  |
| H3×A3×A12 | [5,3,2,3,3,2,2] |  |  |  |
| BC3×BC3×A12 | [4,3,2,4,3,2,2] |  |  |  |
| H3×BC3×A12 | [5,3,2,4,3,2,2] |  |  |  |
| H3×H3×A12 | [5,3,2,5,3,2,2] |  |  |  |
| A3×I2(p)×I2(q)×A1 | [3,3,2,p,2,q,2] |  |  |  |
| BC3×I2(p)×I2(q)×A1 | [4,3,2,p,2,q,2] |  |  |  |
| H3×I2(p)×I2(q)×A1 | [5,3,2,p,2,q,2] |  |  |  |
| A3×I2(p)×A13 | [3,3,2,p,2,2,2] |  |  |  |
| BC3×I2(p)×A13 | [4,3,2,p,2,2,2] |  |  |  |
| H3×I2(p)×A13 | [5,3,2,p,2,2,2] |  |  |  |
| A3×A15 | [3,3,2,2,2,2,2] |  |  |  |
| BC3×A15 | [4,3,2,2,2,2,2] |  |  |  |
| H3×A15 | [5,3,2,2,2,2,2] |  |  |  |
| I2(p)×I2(q)×I2(r)×I2(s) | [p,2,q,2,r,2,s] |  | 16pqrs |  |
| I2(p)×I2(q)×I2(r)×A12 | [p,2,q,2,r,2,2] |  | 32pqr |  |
| I2(p)×I2(q)×A14 | [p,2,q,2,2,2,2] |  | 64pq |  |
| I2(p)×A16 | [p,2,2,2,2,2,2] |  | 128p |  |
| A18 | [2,2,2,2,2,2,2] |  | 256 |  |