Cantellated 6-orthoplexes


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

Cantellated 6-orthoplex

Alternate names

  • Cantellated hexacross
  • Small rhombated hexacontatetrapeton

Construction

There are two Coxeter groups associated with the cantellated 6-orthoplex, one with the B6 or Coxeter group, and a lower symmetry with the D6 or Coxeter group.

Coordinates

Cartesian coordinates for the 480 vertices of a cantellated 6-orthoplex, centered at the origin, are all the sign and coordinate permutations of

Bicantellated 6-orthoplex

Alternate names

  • Bicantellated hexacross, bicantellated hexacontatetrapeton
  • Small birhombated hexacontatetrapeton

Construction

There are two Coxeter groups associated with the bicantellated 6-orthoplex, one with the B6 or Coxeter group, and a lower symmetry with the D6 or Coxeter group.

Coordinates

Cartesian coordinates for the 1440 vertices of a bicantellated 6-orthoplex, centered at the origin, are all the sign and coordinate permutations of

Cantitruncated 6-orthoplex

Alternate names

  • Cantitruncated hexacross, cantitruncated hexacontatetrapeton
  • Great rhombihexacontatetrapeton

Construction

There are two Coxeter groups associated with the cantitruncated 6-orthoplex, one with the B6 or Coxeter group, and a lower symmetry with the D6 or Coxeter group.

Coordinates

Cartesian coordinates for the 960 vertices of a cantitruncated 6-orthoplex, centered at the origin, are all the sign and coordinate permutations of

Bicantitruncated 6-orthoplex

Alternate names

  • Bicantitruncated hexacross, bicantitruncated hexacontatetrapeton
  • Great birhombihexacontatetrapeton

Construction

There are two Coxeter groups associated with the bicantitruncated 6-orthoplex, one with the B6 or Coxeter group, and a lower symmetry with the D6 or Coxeter group.

Coordinates

Cartesian coordinates for the 2880 vertices of a bicantitruncated 6-orthoplex, centered at the origin, are all the sign and coordinate permutations of

Related polytopes

These polytopes are part of a set of 63 uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-cube or 6-orthoplex.