In 6-dimensional geometry, there are 35 uniform polytopes with A_{6} symmetry. There is one self-dual regular form, the 6-simplex with 7 vertices.

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

## Graphs

Symmetric orthographic projections of these 35 polytopes can be made in the A_{6}, A_{5}, A_{4}, A_{3}, A_{2} Coxeter planes. A_{k} graphs have *[k+1]* symmetry. For even k and symmetric ringed diagrams, symmetry doubles to *[2(k+1)]*.

These 63 polytopes are each shown in these 5 symmetry planes, with vertices and edges drawn, and vertices colored by the number of overlapping vertices in each projective position.

## References

A6 polytope Wikipedia(Text) CC BY-SA