In 8-dimensional geometry, there are 255 uniform polytopes with B<sub>8</sub> symmetry (to which this article adds for illustration the 8-demicube as an alternation with half symmetry). There are two regular forms, the 8-orthoplex and 8-cube, with 16 and 256 vertices respectively.
They can be visualized as symmetric orthographic projections in Coxeter planes of the B<sub>8</sub> Coxeter group, and other subgroups.
Symmetric orthographic projections of these 256 polytopes can be made in the B<sub>8</sub>, B<sub>7</sub>, B<sub>6</sub>, B<sub>5</sub>, B<sub>4</sub>, B<sub>3</sub>, B<sub>2</sub>, A<sub>7</sub>, A<sub>5</sub>, A<sub>3</sub>, Coxeter planes. A<sub>k</sub> has [k+1] symmetry, and B<sub>k</sub> has [2k] symmetry.
These 256 polytopes are each shown in these 10 symmetry planes, with vertices and edges drawn, and vertices colored by the number of overlapping vertices in each projective position.