SOLUTION: . A cube has all its corners cut off. How many edges does the resulting shape have?

I will assume 


    a)  that we cut small enough corner parts creating triangular faces at the cuts and 

    b)  that these triangles are/remain disjoint.


Then the new solid has (still keep) 12 native edges of the original cube PLUS 8*3 new edges, by 3 at each of 8 cube's corners.


So the number under the question is 12 + 3*8 = 36 edges.