In 5-dimensional geometry, there are 19 uniform polytopes with A<sub>5</sub> symmetry. There is one self-dual regular form, the 5-simplex with 6 vertices.
Each can be visualized as symmetric orthographic projections in the Coxeter planes of the A<sub>5</sub> Coxeter group and other subgroups.
Symmetric orthographic projections of these 19 polytopes can be made in the A<sub>5</sub>, A<sub>4</sub>, A<sub>3</sub>, A<sub>2</sub> Coxeter planes. A<sub>k</sub> graphs have [k+1] symmetry. For even k and symmetrically nodea_1ed-diagrams, symmetry doubles to [2(k+1)].
These 19 polytopes are each shown in these 4 symmetry planes, with vertices and edges drawn and vertices colored by the number of overlapping vertices in each projective position.