In 8-dimensional geometry, there are 135 uniform polytopes with A_{8} symmetry. There is one self-dual regular form, the 8-simplex with 9 vertices.

Each can be visualized as symmetric orthographic projections in Coxeter planes of the A_{8} Coxeter group, and other subgroups.

Symmetric orthographic projections of these 135 polytopes can be made in the A_{8}, A_{7}, A_{6}, A_{5}, A_{4}, A_{3}, A_{2} Coxeter planes. A_{k} has *[k+1]* symmetry.

These 135 polytopes are each shown in these 7 symmetry planes, with vertices and edges drawn, and vertices colored by the number of overlapping vertices in each projective position.