Pyraminx
The Pyraminx was actually invented before the 3x3x3, in 1967, but its inventor did not realise its potential until the 3x3x3 was popularised. The pyraminx is easier to solve than the 3x3x3 and only has 933,120 combinations if you ignore the trivial tips, the best speedcubers can solve the pyraminx in around 2 seconds on average.
