Twelve directions in space

Description of tetrahedrons

This group of tetrahedrons is generated by paths of the form (4253154253143521543521) and all even permutations of the first four maticies. These paths twist in 12 directions. The odd permutations would end up at the same place but twist in the opposite direction. The ending positions of each arm is in the form of a closest packing of spheres about a central sphere.