Teaser 2835: Jeweller’s rouge

From The Sunday Times, 22nd January 2017 [link]

Fabulé’s latest creation consists of a set of equal-sized silver cubes. On each face of each cube there is one diagonal of identical rubies. No two cubes are the same, but had Fabulé made any more such cubes then it would have been necessary to repeat one of the designs.

How many cubes are there in the set?

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