mathematics – Cover a cube with hugs and kisses!

The total area of the given shapes is 60 square units. Therefore, each face of the cube must be 10 square units. The edge length is the diagonal of a 1 x 3 rectangle. With this in mind, we find this solution:

The four hugs share a common vertex which is the center of one cube face. With the proper orientation, the four kisses can be wrapped around them to cover the cube as desired.