Find the shape and symmetries of the two pieces of this cut cube.
Prove that the graph of f(x) = x^3 - 6x^2 +9x +1 has rotational
symmetry. Do graphs of all cubics have rotational symmetry?
Mark a point P inside a closed curve. Is it always possible to find
two points that lie on the curve, such that P is the mid point of
the line joining these two points?