In six-dimensional geometry, a cantellated 6-orthoplex is a convex uniform 6-polytope, being a cantellation of the regular 6-orthoplex.
There are 8 cantellation for the 6-orthoplex including truncations. Half of them are more easily constructed from the dual 6-cube
There are two Coxeter groups associated with the cantellated 6-orthoplex, one with the B<sub>6</sub> or [4,3,3,3,3] Coxeter group, and a lower symmetry with the D<sub>6</sub> or [3<sup>3,1,1</sup>] Coxeter group.
Cartesian coordinates for the 480 vertices of a cantellated 6-orthoplex, centered at the origin, are all the sign and coordinate permutations of
There are two Coxeter groups associated with the bicantellated 6-orthoplex, one with the B<sub>6</sub> or [4,3,3,3,3] Coxeter group, and a lower symmetry with the D<sub>6</sub> or [3<sup>3,1,1</sup>] Coxeter group.
Cartesian coordinates for the 1440 vertices of a bicantellated 6-orthoplex, centered at the origin, are all the sign and coordinate permutations of
There are two Coxeter groups associated with the cantitruncated 6-orthoplex, one with the B<sub>6</sub> or [4,3,3,3,3] Coxeter group, and a lower symmetry with the D<sub>6</sub> or [3<sup>3,1,1</sup>] Coxeter group.
Cartesian coordinates for the 960 vertices of a cantitruncated 6-orthoplex, centered at the origin, are all the sign and coordinate permutations of
There are two Coxeter groups associated with the bicantitruncated 6-orthoplex, one with the B<sub>6</sub> or [4,3,3,3,3] Coxeter group, and a lower symmetry with the D<sub>6</sub> or [3<sup>3,1,1</sup>] Coxeter group.
Cartesian coordinates for the 2880 vertices of a bicantitruncated 6-orthoplex, centered at the origin, are all the sign and coordinate permutations of
These polytopes are part of a set of 63 uniform 6-polytopes generated from the B<sub>6</sub> Coxeter plane, including the regular 6-cube and 6-orthoplex.