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Daftar grup titik > Seven dimensions

The following table gives the seven-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]+ has six 3-fold gyration points and symmetry order 20160.
| Coxeter group | Coxeter group | Coxeter diagram | Order | Related polytopes |
| --- | --- | --- | --- | --- |
| A7 | [3,3,3,3,3,3] |  | 40320 (8!) | 7-simplex |
| A7×2 | [[3,3,3,3,3,3]] |  | 80640 (2×8!) | 7-simplex dual compound |
| BC7 | [4,3,3,3,3,3] |  | 645120 (27×7!) | 7-cube, 7-orthoplex |
| D7 | [3,3,3,3,31,1] |  | 322560 (26×7!) | 7-demicube |
| E7 | [3,3,3,32,1] |  | 2903040 (8×9!) | 321, 231, 132 |
| A6×A1 | [3,3,3,3,3,2] |  | 10080 (2×7!) |  |
| BC6×A1 | [4,3,3,3,3,2] |  | 92160 (27×6!) |  |
| D6×A1 | [3,3,3,31,1,2] |  | 46080 (26×6!) |  |
| E6×A1 | [3,3,32,1,2] |  | 103680 (144×6!) |  |
| A5×I2(p) | [3,3,3,3,2,p] |  | 1440p |  |
| BC5×I2(p) | [4,3,3,3,2,p] |  | 7680p |  |
| D5×I2(p) | [3,3,31,1,2,p] |  | 3840p |  |
| A5×A12 | [3,3,3,3,2,2] |  | 2880 |  |
| BC5×A12 | [4,3,3,3,2,2] |  | 15360 |  |
| D5×A12 | [3,3,31,1,2,2] |  | 7680 |  |
| A4×A3 | [3,3,3,2,3,3] |  | 2880 |  |
| A4×BC3 | [3,3,3,2,4,3] |  | 5760 |  |
| A4×H3 | [3,3,3,2,5,3] |  | 14400 |  |
| BC4×A3 | [4,3,3,2,3,3] |  | 9216 |  |
| BC4×BC3 | [4,3,3,2,4,3] |  | 18432 |  |
| BC4×H3 | [4,3,3,2,5,3] |  | 46080 |  |
| H4×A3 | [5,3,3,2,3,3] |  | 345600 |  |
| H4×BC3 | [5,3,3,2,4,3] |  | 691200 |  |
| H4×H3 | [5,3,3,2,5,3] |  | 1728000 |  |
| F4×A3 | [3,4,3,2,3,3] |  | 27648 |  |
| F4×BC3 | [3,4,3,2,4,3] |  | 55296 |  |
| F4×H3 | [3,4,3,2,5,3] |  | 138240 |  |
| D4×A3 | [31,1,1,2,3,3] |  | 4608 |  |
| D4×BC3 | [3,31,1,2,4,3] |  | 9216 |  |
| D4×H3 | [3,31,1,2,5,3] |  | 23040 |  |
| A4×I2(p)×A1 | [3,3,3,2,p,2] |  | 480p |  |
| BC4×I2(p)×A1 | [4,3,3,2,p,2] |  | 1536p |  |
| D4×I2(p)×A1 | [3,31,1,2,p,2] |  | 768p |  |
| F4×I2(p)×A1 | [3,4,3,2,p,2] |  | 4608p |  |
| H4×I2(p)×A1 | [5,3,3,2,p,2] |  | 57600p |  |
| A4×A13 | [3,3,3,2,2,2] |  | 960 |  |
| BC4×A13 | [4,3,3,2,2,2] |  | 3072 |  |
| F4×A13 | [3,4,3,2,2,2] |  | 9216 |  |
| H4×A13 | [5,3,3,2,2,2] |  | 115200 |  |
| D4×A13 | [3,31,1,2,2,2] |  | 1536 |  |
| A32×A1 | [3,3,2,3,3,2] |  | 1152 |  |
| A3×BC3×A1 | [3,3,2,4,3,2] |  | 2304 |  |
| A3×H3×A1 | [3,3,2,5,3,2] |  | 5760 |  |
| BC32×A1 | [4,3,2,4,3,2] |  | 4608 |  |
| BC3×H3×A1 | [4,3,2,5,3,2] |  | 11520 |  |
| H32×A1 | [5,3,2,5,3,2] |  | 28800 |  |
| A3×I2(p)×I2(q) | [3,3,2,p,2,q] |  | 96pq |  |
| BC3×I2(p)×I2(q) | [4,3,2,p,2,q] |  | 192pq |  |
| H3×I2(p)×I2(q) | [5,3,2,p,2,q] |  | 480pq |  |
| A3×I2(p)×A12 | [3,3,2,p,2,2] |  | 192p |  |
| BC3×I2(p)×A12 | [4,3,2,p,2,2] |  | 384p |  |
| H3×I2(p)×A12 | [5,3,2,p,2,2] |  | 960p |  |
| A3×A14 | [3,3,2,2,2,2] |  | 384 |  |
| BC3×A14 | [4,3,2,2,2,2] |  | 768 |  |
| H3×A14 | [5,3,2,2,2,2] |  | 1920 |  |
| I2(p)×I2(q)×I2(r)×A1 | [p,2,q,2,r,2] |  | 16pqr |  |
| I2(p)×I2(q)×A13 | [p,2,q,2,2,2] |  | 32pq |  |
| I2(p)×A15 | [p,2,2,2,2,2] |  | 64p |  |
| A17 | [2,2,2,2,2,2] |  | 128 |  |