In 2 dimension, a unit square and a unit rhombus(of certain angle) has the same list of edges and connection status. But the unit square and the unit rhombus are not generally congruent.
Can we find such example in 3 dimension ? I feel it is much harder to find such example in 3d.
I'll express it in more precise way :
Let A be a convex polyhedron and let L be unordered list of all faces of A. Let B be a convex polyhedron and let M be unordered list of all faces of B.
Suppose that L = M and there is 1-1 correspondence between L and M that preserves the connection status. (the term connection status is a little vague but I think we can define them logically precisely) Then can we say A is congruent to B ?