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January 9

24-cell question

If the vertices of a 24-cell are numbered from 1 to 24 *with* all opposite vertices summing to 25 (so for example, if 1,0,1,0 has value 8 then -1,0,-1,0 has value 17 for the situation where the 24-cell vertices are permutations (+/-1,+-/1,0,0)), and each of the octahedral cells has the value equal to the sum of its six vertices, what is the maximum number of octahedral cells which can share the same sum?Naraht (talk) 22:03, 9 January 2019 (UTC)[reply]

There are 24!!/1152 = 1.7 billion possible numberings up to symmetry, which is large but not unreasonable for a brute force computer search. Perhaps is there is a cleverer way but I don't see it. --RDBury (talk) 12:26, 11 January 2019 (UTC)[reply]