Is there a situation in your game, when it has no legal moves? In games like this: Tetris, Match-3, Lines, so on, there is some kind of no-legal moves situation. Usually it's where game ends. I think adjusting rules, so such situation arises may improve gameplay. For example some idea: You can rotate block only if some block pops down during that rotation (either rotating or neighbor). Blocks pop down if at least 3 their sides match sides of neighbor squares. And, yes, you can't exchange color on sides. It's untested, but may serve foundation for more refined version of rules.
The tetris mode does have situations where their are no moves, which is probably another reason i like it alot more over the classic mode. I'll see if i can work your idea, I'm thinking something along the idea that you can only rotate blocks, and they pop if all the sides line up with all the neighbor sides.
How about a snake mode, where you try to connect as many triangles of the same color as you can without making a square?
could you elaborate on this, how would the triangles be considered connected?
I recall from my misspent youth a spatial intelligence test where you had to assemble different shapes together to match the picture provided.
Is your game necessarily limited to the square or can shapes be formed using the triangles as moving, rotating and flipping the shapes provided to match the picture as a Spatial Intelligence mode might be interesting.
or you could provide a template to which people need to match with colours in the right place i.e. 3x3, 4x4 etc using your existing rotating, swapping.
Also the introduction of a novelty triangle which when matched up with 3 other matching novelty triangle unlocks a virtual reward such as a new skin colour.
unfortunately the game is built around the cubes/grid format, so i can't assemble other shapes. I could do something like randomizing a grid, and having players re-build it.
edit: i've implemented WildField's idea(or at the least the interpretation i got, not 100% sure i'm on the same page as he is), anyway, it's a really great addition, matching the surrounding triangles adds a ton of challenge that classic doesn't offer.