students could find a few and maybe draw accurate diagrams (with or without a square cm grid)

you could consider the edges that could be 'unjoined' at various stages (to leave 5 joined)

some sources have argued that there are the same as for a cube (which seems to be quite incorrect)

there appear to be 54 (with a fairly high degree of confidence...)

here's a 'justification' involving an attempt at a systematic approach (enhanced by Puntmat pointing out that I'd missed two of the options ...)

the fine people at Puntmat found two more, to complete trios in the picture above:

so that makes 54, a number that the Puntmat team and I think is a very neat answer....

suggesting that there might be another way of deducing this total (unless someone finds any more options of course...)

anyway, our answer is 54

many thanks to the Puntmat team

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