In 7-dimensional geometry, there are 95 uniform polytopes with D<sub>7</sub> symmetry; 32 are unique, and 63 are shared with the B<sub>7</sub> symmetry. There are two regular forms, the 7-orthoplex, and 7-demicube with 14 and 64 vertices respectively.
They can be visualized as symmetric orthographic projections in Coxeter planes of the D<sub>6</sub> Coxeter group, and other subgroups.
Symmetric orthographic projections of these 32 polytopes can be made in the D<sub>7</sub>, D<sub>6</sub>, D<sub>5</sub>, D<sub>4</sub>, D<sub>3</sub>, A<sub>5</sub>, A<sub>3</sub>, Coxeter planes. A<sub>k</sub> has [k+1] symmetry, D<sub>k</sub> has [2(k-1)] symmetry. B<sub>7</sub> is also included although only half of its [14] symmetry exists in these polytopes.
These 32 polytopes are each shown in these 8 symmetry planes, with vertices and edges drawn, and vertices colored by the number of overlapping vertices in each projective position in progressive order: red, orange, yellow, green, cyan, blue, purple, magenta, red-violet.