Fold Into a Cube

If the size of each of the small edges of the shape is equal to 1cm, then its area is equal to 30cm². Thus, the cube that is formed by the shape must have an edge of length √5cm. If we set the center of the black shape to be the center of one of the cube’s faces, then the four closest vertices must lie on the boundary of the shape, √2.5cm away. This determines uniquely the folding of the shape which is shown on the simulation below.