to start I am not sure if this is the right SE to be posting this so feel free to tell me if I should take it down or change tags.
Now to proceed to the core of my question. I am thinking about my Senior research and I have been inclined toward Groups, to be specific I find permutation groups rather interesting. Besides that I have always been amused by puzzles and games and I know that there is a lot of interesting math behind a number of them.
One of the puzzles I like the most is Pyraminx so I would like to see if my research could involve it in some way. I have searched on arxiv, MSE and google in general and I have found limited amount of work done about it.
I would like to know if there is something interesting left to be done or if it is already been thoroughly researched and I am just bad at gooogling? This is important as I wouldn't want to waste weeks and just then find out that I am doing nothing.
To be specific I would like to look into the permutation group of the game and its subgroups, look at generators, find some bounds on the orders and so on, I am yet to think of something more specific.