In 7-dimensional geometry, there are 71 uniform polytopes with A_{7} symmetry. There is one self-dual regular form, the 7-simplex with 8 vertices.

Each can be visualized as symmetric orthographic projections in Coxeter planes of the A_{7} Coxeter group, and other subgroups.

Symmetric orthographic projections of these 135 polytopes can be made in the A_{7}, A_{6}, A_{5}, A_{4}, A_{3}, A_{2} Coxeter planes. A_{k} has *[k+1]* symmetry. For even *k* and symmetrically ringed-diagrams, symmetry doubles to *[2(k+1)]*.

These 63 polytopes are each shown in these 6 symmetry planes, with vertices and edges drawn, and vertices colored by the number of overlapping vertices in each projective position.