# E6 polytope

In 6-dimensional geometry, there are 39 uniform polytopes with E_{6} symmetry. The two simplest forms are the 2_{21} and 1_{22} polytopes, composed of 27 and 72 vertices respectively.

They can be visualized as symmetric orthographic projections in Coxeter planes of the E_{6} Coxeter group, and other subgroups.

Symmetric orthographic projections of these 39 polytopes can be made in the E_{6}, D_{5}, D_{4}, D_{2}, A_{5}, A_{4}, A_{3} Coxeter planes. A_{k} has *k+1* symmetry, D_{k} has *2(k-1)* symmetry, and E_{6} has *12* symmetry.

Six symmetry planes graphs are shown for 9 of the 39 polytopes in the E_{6} symmetry. The vertices and edges drawn with vertices colored by the number of overlapping vertices in each projective position.