nLab
hosohedron
ADE classification
and
McKay correspondence
Dynkin diagram
/
Dynkin quiver
dihedron
,
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
$SU(n+1)$
A1
cyclic group of order 2
$\mathbb{Z}_2$
cyclic group of order 2
$\mathbb{Z}_2$
SU(2)
A2
cyclic group of order 3
$\mathbb{Z}_3$
cyclic group of order 3
$\mathbb{Z}_3$
SU(3)
A3
=
D3
cyclic group of order 4
$\mathbb{Z}_4$
cyclic group of order 4
$2 D_2 \simeq \mathbb{Z}_4$
SU(4)
$\simeq$
Spin(6)
D4
dihedron
on
bigon
Klein four-group
$D_4 \simeq \mathbb{Z}_2 \times \mathbb{Z}_2$
quaternion group
$2 D_4 \simeq$
Q8
SO(8)
,
Spin(8)
D5
dihedron
on
triangle
dihedral group of order 6
$D_6$
binary dihedral group of order 12
$2 D_6$
SO(10)
,
Spin(10)
D6
dihedron
on
square
dihedral group of order 8
$D_8$
binary dihedral group of order 16
$2 D_{8}$
SO(12)
,
Spin(12)
$D_{n \geq 4}$
dihedron
,
hosohedron
dihedral group
$D_{2(n-2)}$
binary dihedral group
$2 D_{2(n-2)}$
special orthogonal group
,
spin group
$SO(2n)$
,
$Spin(2n)$
$E_6$
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
References
See also
Wikipedia,
Hosohedron