MAn have people to this point missed the point with higher dimensional perspective.
If you want a little dimensional problem . see what regular polygons you can get a given number of to connect up such that each side of the polygon connects to a unique polygon in such a way that all sides are connected. you can play the game of finding new groups of a given number of the same or two different polygons by arranging the polygons flat you want to play with on your piece of paper and connecting one side to one side never linking a side that has already been linked.
It's the rules for a game called find the 2 polygon or one polygon group that follows the rules and you Hsve lightly found a solid in some dimension.
If you can program math why not test with the computer how hard the task is just with bruit force not that hard actually until your talking like 3 groups of 40 and above polygons by which time you may be able to predict such solids faster than bruit force.
Let the search for regular polygon surface solids be with you