This is a sequel to this posting:viewtopic.php?f=15&t=24813
These four variants all implement one out of 33 subgroups known to the group of octahedral symmetry.
Since the topic is very abstract the four puzzles bear abstract names.
Top left: "AsymCorners 84210" which implements the subgroup with 90°-rotation.
Top right: "AsymCorners 40020000000000000000080010" which implements the subgroups with all three 180°-center-rotations.
Bottom left: "SharpCorners 44000" which implements the subgroup with two orthogonal reflections on planes through opposite edges.
Bottom right: "AsymCorners 10400000000000004040000" which implements the subgroup with a central spiral.
If you want to see the completed series, please refere to this thread