1752: Euler proposes relation
of Verticies, Edges, and Faces:

V - E + F = 2. Polyhedra are defined as "a solid whose faces are polygons."

1815: Hessel notes that
a cube with a cubic hollow inside does not satisfy Euler's theorem. Polyhedra
are redefined as "a surface made up of polygonal faces."

1865: Mobius notes that two
pyramids joined a tthe vertex also defies Euler's theorem. Polyhedra are
redefined as "a system of polygons such that two polygons meet at every
edge and where it is possible to get from one face to the other without
passing through a vertex."