+ Orthographic projections in the B8 Coxeter plane8-cube8-orthoplex8-demicube In 8-dimensional geometry, there are 255 uniform polytopes with B8 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 B8 Coxeter group, and other subgroups. __TOC__
Graphs Symmetric orthographic projections of these 256 polytopes can be made in the B8, B7, B6, B5, B4, B3, B2, A7, A5, A3, Coxeter planes. Ak has [k+1] symmetry, and Bk has [2k] symmetry.
Each of these 256 polytopes is shown in these 10 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.