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 suggest there are 11 different ways, arguing that there are the same as for a cube

there seem to be 54

here's a 'justification' involving an attempt at a systematic approach (enhanced by Puntmat pointing out that I'd missed 2 ...)

the fine people at Puntmat found 2 more, to complete trios in the picture above:

so that makes 54, a number that the Puntmat team and I think is a 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 Puntmat

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