Painting a Dodecahedron
Each of the 12 faces of a regular dodecahedron is painted one of 3 colours (repeats allowed, not all colours need be used). Two painted dodecahedra are the same if a rotation carries one to the other. How many different painted dodecahedra are there? Give an integer.
Related problems & prerequisites
Worth solving first
- Colouring the Edges of a Cube 6.0/10
- Black and White Corners 6.0/10
- Rotating a Three-by-Three Grid 6.0/10
Source: Standard application of Burnside's lemma; no traceable original source. Statement written for AxiomIQ.