Other forms [of Goldberg polyhedra] can be described by taking a chess knight move from one pentagon to the next: first take $m$ steps in one direction, then turn $60^\circ$ to the left and take $n$ steps. Such a polyhedron is denoted $GP(m,n)$.
I'm trying to convert this to octahedral Goldberg polyhedra, having squares and hexagons. So I would start from a square. But what are steps?
Do they mean $m$ chess knight moves? On a spherical chess board build out of squares and hexagons? Shall I turn by $90^\circ$ if I jump to another square? Turn left or right?...
$\hskip1.9in$ Sorry, I don't play chess that way...
Can anyone explain this to me?
Rules are the same as in the icosahedral case: start from a square and look for the shortest path to another square, using a "chess knight" move. That is: go ahead for $n$ hexagons, turn left by 60° and go on for other $m$ hexagons. This polyhedron is then labeled $(n,m)$.
This polyhedron below, for instance, is labeled $(4,0)$, because if you start from a square and go ahead, after four steps you arrive at the nearest square:
This other polyhedron is labeled $(2,2)$, because to get to the nearest square you must first go ahead two hexagons, then turn left (or right) by one side (60°) and go straight on for two more hexagons: