Properly Painted Cubes
Five colours are available. Each face of a cube is painted with one colour so that any two faces sharing an edge receive different colours (opposite faces may match, and not all colours need be used). Two painted cubes are the same if one can be rotated to match the other. How many different cubes are there? Give an integer.
Related problems & prerequisites
Worth solving first
- Painting a Cube in Three Colours 7.0/10
- Painting a Tetrahedron 7.0/10
- Painting a Dodecahedron 7.0/10
Source: Original problem written for AxiomIQ.