Perhaps many of you have played the game of Tetris, which was closely connected to pentominoes. I spent many hours doing so, and if I had been wise, could have made a lot of money from it...but that is another story to remain untold here....
By luck, I found another interesting game that involves a great amount of geometry. Called Bloxorz, the game was invented by Damien Clarke in June of 2007. Plus, more than 222,500 people have already played it on-line. So, you can see I am a little slow in discovering it.
A rectangular-type block is the focus of Bloxorz. You control and move the block by flipping it sideways or end-over-end through the various mazes of square tiles, with the gola being to plan your moves so that on your last end-over-end flip, the block slides through a square hole. Rather than describing further either the game or the underlying geometry, I suggest you go to the site, read the instructions, and start playing. The geometrical connections will become immediately apparent (and thereby justify your playing the game). On return sittings, use the pass-codes to bypass early "conquered stages."
I learned of the game from a mathematics educator in England, who was complaining about the amount of time she spent (not wasted) playing the game. Try Bloxorz...you might like it...and you have all summer to master its 30+-stages before showing the game to students next year!
If you know of other mathematics-based games on-line such as Bloxorz, please let me know about them so I can share them with others.