Cartesian Coordinates
Cartesian coordinates for the 12 vertices of a truncated tetrahedron centered at the origin, with edge length √8, are all permutations of (±1,±1,±3) with an even number of minus signs:
- (+3,+1,+1), (+1,+3,+1), (+1,+1,+3)
- (−3,−1,+1), (−1,−3,+1), (−1,−1,+3)
- (−3,+1,−1), (−1,+3,−1), (−1,+1,−3)
- (+3,−1,−1), (+1,−3,−1), (+1,−1,−3)
Another simple construction exists in 4-space as cells of the truncated 16-cell, with vertices as coordinate permutation of:
- (0,0,1,2)
| The set of vertex permutations (±1,±1,±3) with an odd number of minus signs forms a complementary truncated tetrahedron, and combined they form a uniform compound polyhedron. |
Read more about this topic: Truncated Tetrahedron