Rubik's Cube has 54 Facets

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
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