Solution of the Week #334 - Skeleton Cube

When viewed such that the cubes where the spheres are centred are at the top and bottom of the figure, those points are square root of 3 apart. The unit lengths lines from the top and bottom vertices describe the extent of the overlap of the two spheres (they are actually cone shaped but from this angle appear to be equilateral triangles). The circle in the middle of the cube is viewed here edge-on, and so its diameter is 1.

cube without spheres sol.jpg