The question explains itself by reading the attached work sheet.
Did we do that in Mathcad ... no recollection ?

Thanks if you have it to try ... Jean

Rotate Quaternion Permute.sm (22 KiB) downloaded 47 time(s).

Valery Ochov did it from his server,
no more access to it.

Rotate Quaternion Permute.sm (28 KiB) downloaded 49 time(s).