Gerard Westendorp on Nostr: The set of 30 possible dice. Together with the 24 ways of orienting each die, they ...

The set of 30 possible dice. Together with the 24 ways of orienting each die, they form the 30X24=720 elements of S6, the group of permutations of 6 objects. I posted a couple of other pictures relating to this lately.
There is a nice weblog by Peter Cameron on this:https://cameroncounts.wordpress.com/2010/05/11/the-symmetric-group-3/
He writes that he used to have a set of 30 dice like this, but lost them.
The arrangement of the dice has some special properties:
In each row and column, each opposite pair occurs once and only once. This means that the rows and columns are “synthematic totals”, as Peter Cameron explains.
The dice on opposite sides of the diagonal are mirror images.