Seven Dimensions
The seven-dimensional point groups, limiting to purely reflectional groups, can be listed by their Coxeter group. Related pure rotational 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 + has six 3-fold gyration points and symmetry order 20160.
| Coxeter group | Coxeter diagram | Order | Related polytopes | |
|---|---|---|---|---|
| A7 | 40320 (8!) | 7-simplex | ||
| A7×2 | ] | 80640 (2×8!) | 7-simplex dual compound | |
| BC7 | 645120 (27×7!) | 7-cube, 7-orthoplex | ||
| D7 | 322560 (26×7!) | 7-demicube | ||
| E7 | 2903040 (8×9!) | 321, 231, 132 | ||
| A6×A1 | 10080 (2×7!) | |||
| BC6×A1 | 92160 (27×6!) | |||
| D6×A1 | 46080 (26×6!) | |||
| E6×A1 | 103680 (144×6!) | |||
| A5×I2(p) | 1440p | |||
| BC5×I2(p) | 7680p | |||
| D5×I2(p) | 3840p | |||
| A5×A12 | 2880 | |||
| BC5×A12 | 15360 | |||
| D5×A12 | 7680 | |||
| A4×A3 | 2880 | |||
| A4×BC3 | 5760 | |||
| A4×H3 | 14400 | |||
| BC4×A3 | 9216 | |||
| BC4×BC3 | 18432 | |||
| BC4×H3 | 46080 | |||
| H4×A3 | 345600 | |||
| H4×BC3 | 691200 | |||
| H4×H3 | 1728000 | |||
| F4×A3 | 27648 | |||
| F4×BC3 | 55296 | |||
| F4×H3 | 138240 | |||
| D4×A3 | 4608 | |||
| D4×BC3 | 9216 | |||
| D4×H3 | 23040 | |||
| A4×I2(p)×A1 | 480p | |||
| BC4×I2(p)×A1 | 1536p | |||
| D4×I2(p)×A1 | 768p | |||
| F4×I2(p)×A1 | 4608p | |||
| H4×I2(p)×A1 | 57600p | |||
| A4×A13 | 960 | |||
| BC4×A13 | 3072 | |||
| F4×A13 | 9216 | |||
| H4×A13 | 115200 | |||
| D4×A13 | 1536 | |||
| A32×A1 | 1152 | |||
| A3×BC3×A1 | 2304 | |||
| A3×H3×A1 | 5760 | |||
| BC32×A1 | 4608 | |||
| BC3×H3×A1 | 11520 | |||
| H32×A1 | 28800 | |||
| A3×I2(p)×I2(q) | 96pq | |||
| BC3×I2(p)×I2(q) | 192pq | |||
| H3×I2(p)×I2(q) | 480pq | |||
| A3×I2(p)×A12 | 192p | |||
| BC3×I2(p)×A12 | 384p | |||
| H3×I2(p)×A12 | 960p | |||
| A3×A14 | 384 | |||
| BC3×A14 | 768 | |||
| H3×A14 | 1920 | |||
| I2(p)×I2(q)×I2(r)×A1 | 16pqr | |||
| I2(p)×I2(q)×A13 | 32pq | |||
| I2(p)×A15 | 64p | |||
| A17 | 128 | |||
Read more about this topic: Point Group
Famous quotes containing the word dimensions:
“I was surprised by Joe’s asking me how far it was to the Moosehorn. He was pretty well acquainted with this stream, but he had noticed that I was curious about distances, and had several maps. He and Indians generally, with whom I have talked, are not able to describe dimensions or distances in our measures with any accuracy. He could tell, perhaps, at what time we should arrive, but not how far it was.”
—Henry David Thoreau (1817–1862)
“Why is it that many contemporary male thinkers, especially men of color, repudiate the imperialist legacy of Columbus but affirm dimensions of that legacy by their refusal to repudiate patriarchy?”
—bell hooks (b. c. 1955)