a vertex of the unit cube is said to be visible from P if it can be connected to P by a straight line that does not pass through the cube.

from any point P outside a unit cube, 4,6, or 7 vertices are visible in the same sense as in the case of the square. Connecting point P to each of these vertices gives 1,2, or 3 square-based pyramids, which make up the visible volume of P. determine the surface area of set of all points P for which the visible volume is 20, and is a polyhedron.