Twisting Puzzles
Skewb
The skewb is shaped like a cube but works a lot more like the pyraminx. It is based on an 8-armed core and takes a little strategy to solve.
The skewb is a Meffert's puzzle and has a fair few mass-produced relatives. The mechanism is also used by people who make custom and modified puzzles because of the way it turns.
Skewbs are relatively easy to solve - you can work out a method if you keep at it for long enough. Algorithms are fairly easy to learn to get past the stages you find difficult and finish the puzzle.