The user interface tries to stay out of the way and still give you all the options you need when solving your puzzles.

Have a look at the UI - cheatsheet :

This cheatsheet is in the game ! Just go to the menu -> storage & setting -> UI Cheatsheet.

As you can see there is a lot of functionality in your touch gestures !

One is actually missing : touch&hold on the solution will open the puzzle menu, just like a double tap.
Also if you happen to tap the rotator number on the lower right, you'll get a bit of an insight into that rotation type.