dodecahedron

**ADE classification** and **McKay correspondence**

Dynkin diagram/ Dynkin quiver | Platonic solid | finite subgroups of SO(3) | finite subgroups of SU(2) | simple Lie group |
---|---|---|---|---|

$A_{n \geq 1}$ | cyclic group $\mathbb{Z}_{n+1}$ | cyclic group $\mathbb{Z}_{n+1}$ | special unitary group $SU(n+1)$ | |

D4 | Klein four-group $D_4 \simeq \mathbb{Z}_2 \times \mathbb{Z}_2$ | quaternion group $2 D_4 \simeq$ Q8 | SO(8) | |

$D_{n \geq 4}$ | dihedron, hosohedron | dihedral group $D_{2(n-2)}$ | binary dihedral group $2 D_{2(n-2)}$ | special orthogonal group $SO(2n)$ |

$E_6$ | tetrahedron | tetrahedral group $T$ | binary tetrahedral group $2T$ | E6 |

$E_7$ | cube, octahedron | octahedral group $O$ | binary octahedral group $2O$ | E7 |

$E_8$ | dodecahedron, icosahedron | icosahedral group $I$ | binary icosahedral group $2I$ | E8 |

- Wikipedia,
*Dodecahedron*

Created on August 18, 2015 at 19:47:13. See the history of this page for a list of all contributions to it.