Polygon touches in more than one point with Shapely

If you truly want to check if two polygons share more than x number of points you can simply do this:

p0,p1,p2 = polygons
x = 2
len(set(p1.boundary.coords).intersection(p2.boundary.coords))>=x

But I think what you may want is to determine if two edges are colinear (and overlapping).

This implementation of Andrew's suggestions is probably what you are looking for:

>>> type(p0.intersection(p1)) is geometry.LineString
True
>>> type(p1.intersection(p2)) is geometry.LineString
False

i haven't used shapely, but have you tried seeing if the intersection of the two polygons is a line?