nLab
tetrahedron

Idea

A 3-simplex. One of the platonic solids.

Related concepts

ADE classification

Dynkin diagram via McKay correspondence	Platonic solid	finite subgroups of SO(3)	finite subgroups of SU(2)	simple Lie group
$A_n$		cyclic group $\mathbb{Z}_{n+1}$	cyclic group $\mathbb{Z}_{n+1}$	special unitary group
$D_{n+4}$	dihedron, hosohedron	dihedral group $D_{n+2}$	binary dihedral group $2 D_{n+2}$	special orthogonal group
$E_6$	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

Related concepts

• circle

• triangle

• square

References

• Felix Klein, chapter I.6 of Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen vom fünften Grade, 1884, translated as Lectures on the Icosahedron and the Resolution of Equations of Degree Five by George Morrice 1888, online version

.