Rubik's Cube has 54 Facets
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Theorem
Let $S$ be the set of facets of Rubik's cube.
Then the cardinality of $S$ is given by:
- $\card S = 54$
That is:
- A Rubik's cube has $54$ facets.
Proof
A cube, by definition, has $6$ faces.
Each face is subdivided into $9$ facets.
Hence there are $6 \times 9 = 54$ facets in total.
$\blacksquare$
Sources
- 2008: David Joyner: Adventures in Group Theory (2nd ed.) ... (previous) ... (next): Chapter $1$: Elementary, my dear Watson: $\S 1.2$: Elements, my dear Watson