In 5-dimensional geometry, there are 23 uniform polytopes with D<sub>5</sub> symmetry, 8 are unique, and 15 are shared with the B<sub>5</sub> symmetry. There are two special forms, the 5-orthoplex, and 5-demicube with 10 and 16 vertices respectively.
They can be visualized as symmetric orthographic projections in Coxeter planes of the D<sub>5</sub> Coxeter group, and other subgroups.
Symmetric orthographic projections of these 8 polytopes can be made in the D<sub>5</sub>, D<sub>4</sub>, D<sub>3</sub>, A<sub>3</sub>, Coxeter planes. A<sub>k</sub> has [k+1] symmetry, D<sub>k</sub> has [2(k-1)] symmetry. The B<sub>5</sub> plane is included, with only half the [10] symmetry displayed.
These 8 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.