If a 3d modeler needs to get rid of polygons in a 3D mesh, but don’t want to add triangles, here’s two good ways. I call them “3-to-1” and “2-to-1 corner”.  I worked these out in 1988 with Joe Formicola and Ken Fedeson, building finite element models for CFD and FEA.  Many other 3d artists have discovered or learned these topological tricks, since (and probably before then, too).  I just noticed how the first one resembles the shadow of a hypercube.