In the course of porting the Wumpus game to JS, I took a look at how the icosahedral world is mapped, and came up with an alternate way to represent it using rings. In the course of doing this, I determined that alternate wumpus worlds could exist with a similar geometry.
Wumpus world exists on a series of at least two rings. The original uses three rings. The innermost and outermost rings will have the same number of nodes. The original has five, but the number can be as low as 2.
The rings between the innermost and outermost will have twice as many nodes as the innermost or outermost.
So, if we describe the various wumpus universes in terms of number of rings and nodes in the innermost ring, we might say that the original is in wumpus universe 3-5.
And because something like this cannot be complete without a formula… the number of nodes in wumpus universe x-y is 2*(x-1)*y.
Nerdy geometry post complete.