File:3d Symmetries vertex.png
Summary
Cubic grid symmetries fixing a vertex. 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_ek"[style=filled]
"C2_ek" -> "C1"
"C2_fk"[style=filled]
"C2_fk" -> "C1"
"CC2_/"[style=filled]
"CC2_/" -> "C1"
"±C1_k" -> "C1"
"CC2_f"[style=filled]
"CC2_f" -> "C1"
"C3"[style=filled]
"C3" -> "C1"
"D4_ke" -> "C2_ek"
"C4_ek"[style=filled]
"C4_ek" -> "C2_ek"
"CC4_ke" -> "C2_ek"
"CD4_ekd"[style=filled]
"CD4_ekd" -> "C2_ek"
"CD4_ekd" -> "CC2_/"
"CD4_fk"[style=filled]
"CD4_fk" -> "CC2_f"
"CD4_fk" -> "CC2_/"
"CD4_fk" -> "C2_fk"
"±C2_kf" -> "CC2_/"
"±C2_kf" -> "±C1_k"
"±C2_kf" -> "C2_fk"
"±C2_ke" -> "C2_ek"
"±C2_ke" -> "CC2_f"
"±C2_ke" -> "±C1_k"
"CD4_eko"[style=filled]
"CD4_eko" -> "CC2_f"
"CD4_eko" -> "C2_ek"
"D4_kf" -> "C2_ek"
"D4_kf" -> "C2_fk"
"CD6"[style=filled]
"CD6" -> "C3"
"CD6" -> "CC2_/"[color=blue]
"D6_k" -> "C3"
"D6_k" -> "C2_fk"[color=blue]
"±C3_k" -> "C3"
"±C3_k" -> "±C1_k"
"±D4_ke" -> "CD4_eko"
"±D4_ke" -> "±C2_ke"
"±D4_ke" -> "D4_ke"
"±C4_ke" -> "±C2_ke"
"±C4_ke" -> "C4_ek"
"±C4_ke" -> "CC4_ke"
"±D4_kf" -> "CD4_ekd"
"±D4_kf" -> "±C2_ke"
"±D4_kf" -> "D4_kf"
"±D4_kf" -> "CD4_fk"
"±D4_kf" -> "±C2_kf"
"DD8_kf" -> "CC4_ke"
"DD8_kf" -> "CD4_eko"
"DD8_kf" -> "D4_kf"
"DD8_ke" -> "CD4_ekd"
"DD8_ke" -> "D4_ke"
"DD8_ke" -> "CC4_ke"
"CD8_ek"[style=filled]
"CD8_ek" -> "C4_ek"
"CD8_ek" -> "CD4_eko"
"CD8_ek" -> "CD4_ekd"
"D8_k" -> "C4_ek"
"D8_k" -> "D4_ke"
"D8_k" -> "D4_kf"
"±D6_k" -> "±C3_k"
"±D6_k" -> "CD6"
"±D6_k" -> "D6_k"
"±D6_k" -> "±C2_kf"[color=blue]
"T12_k" -> "D4_ke"
"T12_k" -> "C3"[color=blue]
"±D8_k" -> "CD8_ek"
"±D8_k" -> "±D4_ke"
"±D8_k" -> "DD8_kf"
"±D8_k" -> "D8_k"
"±D8_k" -> "±C4_ke"
"±D8_k" -> "DD8_ke"
"±D8_k" -> "±D4_kf"
"±T12_k" -> "T12_k"
"±T12_k" -> "±D4_ke"
"±T12_k" -> "±C3_k"[color=blue]
"TO24_k" -> "T12_k"
"TO24_k" -> "DD8_ke"[color=blue]
"TO24_k" -> "CD6"[color=blue]
"O24_k" -> "T12_k"
"O24_k" -> "D8_k"[color=blue]
"O24_k" -> "D6_k"[color=blue]
"±O24_k" -> "±T12_k"
"±O24_k" -> "TO24_k"
"±O24_k" -> "O24_k"
"±O24_k" -> "±D8_k"[color=blue]
"±O24_k" -> "±D6_k"[color=blue]
}
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 05:05, 20 July 2026 | | 1,457 × 539 (217 KB) | Gzaytman (talk | contribs) | |
| 16:10, 19 July 2026 |  | 1,457 × 539 (216 KB) | Gzaytman (talk | contribs) | Cubic grid symmetries fixing a vertex. Blue arrows correspond to non-normal subgroups. Generated using Graphviz from the following input file: digraph symmetries { "C1" "CC2_/" -> "C1" "C2_ek" -> "C1" "C2_fe" -> "C1" "CC2_f" -> "C1" "±C1_e" -> "C1" "C2_ce" -> "C1" "CC2_c" -> "C1" "±C2_ef" -> "CC2_f" "±C2_ef" -> "±C1_e" "±C2_ef" -> "C2_fe" "CD4_fe" -> "CC2_f" "CD4_fe" -> "C2_fe" "CD4_fe" -> "CC2_c" "CD4_ce" -> "CC2_/" "CD4_ce" -> "C2_ce" "CD4_ce" -> "CC2_c" "±C2_ec" -> "CC... |
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