File:3d Symmetries cell.png
Summary
Cubic grid symmetries fixing a cell. Shaded nodes are symmetries that are in at least one of the other graphs. Blue arrows correspond to non-normal subgroups.
Generated using Graphviz from the following input file:
digraph symmetries {
"C1"[style=filled]
"C2_cf"[style=filled]
"C2_cf" -> "C1"
"C2_ce"[style=filled]
"C2_ce" -> "C1"
"CC2_/"[style=filled]
"CC2_/" -> "C1"
"±C1_c" -> "C1"
"CC2_c"[style=filled]
"CC2_c" -> "C1"
"C3"[style=filled]
"C3" -> "C1"
"D4_cf" -> "C2_cf"
"C4_cf"[style=filled]
"C4_cf" -> "C2_cf"
"CC4_cf" -> "C2_cf"
"CD4_cfd"[style=filled]
"CD4_cfd" -> "C2_cf"
"CD4_cfd" -> "CC2_/"
"CD4_ce"[style=filled]
"CD4_ce" -> "CC2_c"
"CD4_ce" -> "CC2_/"
"CD4_ce" -> "C2_ce"
"±C2_ce" -> "CC2_/"
"±C2_ce" -> "±C1_c"
"±C2_ce" -> "C2_ce"
"±C2_cf" -> "C2_cf"
"±C2_cf" -> "CC2_c"
"±C2_cf" -> "±C1_c"
"CD4_cfo"[style=filled]
"CD4_cfo" -> "CC2_c"
"CD4_cfo" -> "C2_cf"
"D4_ce" -> "C2_cf"
"D4_ce" -> "C2_ce"
"CD6"[style=filled]
"CD6" -> "C3"
"CD6" -> "CC2_/"[color=blue]
"D6_c" -> "C3"
"D6_c" -> "C2_ce"[color=blue]
"±C3_c" -> "C3"
"±C3_c" -> "±C1_c"
"±D4_cf" -> "CD4_cfo"
"±D4_cf" -> "±C2_cf"
"±D4_cf" -> "D4_cf"
"±C4_cf" -> "±C2_cf"
"±C4_cf" -> "C4_cf"
"±C4_cf" -> "CC4_cf"
"±D4_ce" -> "CD4_cfd"
"±D4_ce" -> "±C2_cf"
"±D4_ce" -> "D4_ce"
"±D4_ce" -> "CD4_ce"
"±D4_ce" -> "±C2_ce"
"DD8_ce" -> "CC4_cf"
"DD8_ce" -> "CD4_cfo"
"DD8_ce" -> "D4_ce"
"DD8_cf" -> "CD4_cfd"
"DD8_cf" -> "D4_cf"
"DD8_cf" -> "CC4_cf"
"CD8_cf"[style=filled]
"CD8_cf" -> "C4_cf"
"CD8_cf" -> "CD4_cfo"
"CD8_cf" -> "CD4_cfd"
"D8_c" -> "C4_cf"
"D8_c" -> "D4_cf"
"D8_c" -> "D4_ce"
"±D6_c" -> "±C3_c"
"±D6_c" -> "CD6"
"±D6_c" -> "D6_c"
"±D6_c" -> "±C2_ce"[color=blue]
"T12_c" -> "D4_cf"
"T12_c" -> "C3"[color=blue]
"±D8_c" -> "CD8_cf"
"±D8_c" -> "±D4_cf"
"±D8_c" -> "DD8_ce"
"±D8_c" -> "D8_c"
"±D8_c" -> "±C4_cf"
"±D8_c" -> "DD8_cf"
"±D8_c" -> "±D4_ce"
"±T12_c" -> "T12_c"
"±T12_c" -> "±D4_cf"
"±T12_c" -> "±C3_c"[color=blue]
"TO24_c" -> "T12_c"
"TO24_c" -> "DD8_cf"[color=blue]
"TO24_c" -> "CD6"[color=blue]
"O24_c" -> "T12_c"
"O24_c" -> "D8_c"[color=blue]
"O24_c" -> "D6_c"[color=blue]
"±O24_c" -> "±T12_c"
"±O24_c" -> "TO24_c"
"±O24_c" -> "O24_c"
"±O24_c" -> "±D8_c"[color=blue]
"±O24_c" -> "±D6_c"[color=blue]
}
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 04:58, 20 July 2026 | | 1,436 × 539 (216 KB) | Gzaytman (talk | contribs) | |
| 16:06, 19 July 2026 |  | 1,436 × 539 (214 KB) | Gzaytman (talk | contribs) | Cubic grid symmetries fixing a cell. Blue arrows correspond to non-normal subgroups. Generated using Graphviz from the following input file: digraph symmetries { "C1" "C2_cf" -> "C1" "C2_ce" -> "C1" "CC2_/" -> "C1" "±C1_c" -> "C1" "CC2_c" -> "C1" "C3" -> "C1" "D4_cf" -> "C2_cf" "C4_cf" -> "C2_cf" "CC4_cf" -> "C2_cf" "CD4_cfd" -> "C2_cf" "CD4_cfd" -> "CC2_/" "CD4_ce" -> "CC2_c" "CD4_ce" -> "CC2_/" "CD4_ce" -> "C2_ce" "±C2_ce" -> "CC2_/" "±C2_ce" -> "±C1_c" "±C2_ce" -> "C2_... |
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