Finite groups · Family
Exceptional binary polyhedral groups
The binary tetrahedral, octahedral and icosahedral groups.
Reference coverageFinite families
Definition
The inverse images in SU(2) of the tetrahedral, octahedral and icosahedral rotation groups under SU(2) → SO(3).
Definition sourcesParameter domain
The binary tetrahedral, octahedral and icosahedral groups.
| Parameter | Allowed values |
|---|---|
| G | 2T, 2O or 2I |
Reference properties
Related objects and maps
- Finite subgroups of SU(2)
Claims and sources
Each assertion has a stable identifier within this record and a source locator or derivation. Cite the dataset edition when referring to a corrected or historical claim.
Definition
The inverse images in SU(2) of the tetrahedral, octahedral and icosahedral rotation groups under SU(2) → SO(3).
- Character Theory of Finite Groups: Day 4 — The McKay CorrespondenceBinary polyhedral groups, slides 7–8Open source
- GroupNames: SL(2,3), binary tetrahedralAliases: binary polyhedral group; Centre and rotational quotientOpen source
- GroupNames: CSU(2,3), binary octahedralAliases: binary polyhedral group; Centre and rotational quotientOpen source
- GroupNames: SL(2,5), binary icosahedralAliases: binary polyhedral group; Centre and rotational quotientOpen source
family:binary-polyhedral#definitionParameter domain
G: 2T, 2O or 2I
- Character Theory of Finite Groups: Day 4 — The McKay CorrespondenceBinary polyhedral groups, slides 7–8Open source
- GroupNames: SL(2,3), binary tetrahedralAliases: binary polyhedral group; Centre and rotational quotientOpen source
- GroupNames: CSU(2,3), binary octahedralAliases: binary polyhedral group; Centre and rotational quotientOpen source
- GroupNames: SL(2,5), binary icosahedralAliases: binary polyhedral group; Centre and rotational quotientOpen source
family:binary-polyhedral#parametersScope and restrictions
The binary tetrahedral, octahedral and icosahedral groups.
- Character Theory of Finite Groups: Day 4 — The McKay CorrespondenceBinary polyhedral groups, slides 7–8Open source
- GroupNames: SL(2,3), binary tetrahedralAliases: binary polyhedral group; Centre and rotational quotientOpen source
- GroupNames: CSU(2,3), binary octahedralAliases: binary polyhedral group; Centre and rotational quotientOpen source
- GroupNames: SL(2,5), binary icosahedralAliases: binary polyhedral group; Centre and rotational quotientOpen source
family:binary-polyhedral#restrictionFinite subgroups of SU(2)
group:su-2
- Character Theory of Finite Groups: Day 4 — The McKay CorrespondenceBinary polyhedral groups, slides 7–8Open source
- GroupNames: SL(2,3), binary tetrahedralAliases: binary polyhedral group; Centre and rotational quotientOpen source
- GroupNames: CSU(2,3), binary octahedralAliases: binary polyhedral group; Centre and rotational quotientOpen source
- GroupNames: SL(2,5), binary icosahedralAliases: binary polyhedral group; Centre and rotational quotientOpen source
family:binary-polyhedral#relation-1