An interesting math problem

Verify the regular solid shapes only can be five types.
证明正多面体只能有5种.
First: Look at the proof procedure below:

 1*/

Yes, it's just so easy :0
Then I try to carve it out with code
Second: The easiest solution

 1        static void GetResult()
 2        }

Also, it's very easy, and I'm sure it is not a good methd. The biggest problem is that the efficiency is so low.
It must has better solutions to solve this question.
Log it here and fix the efficiency problem later.