The challenge is to cover the surface of a cube using pentominoes. If we allow the pieces to bend around the edges, then cubes with non-integer edges can be covered.
Edge Length = √5
 |
 |
 |
 |
 |
 |
 |
 |
| F | N | P | U |
 |
 |
 |
 |
 |
 |
 |
 |
| *W | X | Y | Z |
*W solution improved by George Sicherman
Edge Length = √10
 |
 |
 |
 |
 |
 |
| F | I | L |
 |
 |
 |
 |
 |
 |
| N | P | T |
 |
 |
 |
 |
 |
 |
| V | Y | Z |
Edge Length = 2√5
 |
 |
 |
 |
 |
 |
| F | P | T |
 |
 |
 |
 |
 |
 |
| V | X | Y |
 |
||
 |
||
| Z |
Edge Length = 5
 |
 |
 |
 |
 |
 |
| F | I | L |
 |
 |
 |
 |
 |
 |
| P | X | *Y |
*Y by George Sicherman