a     = alpha + I beta - gamma - I delta
astar = alpha - I beta - gamma + I delta
b     = alpha + I beta - delta - I gamma
bstar = alpha - I beta - delta + I gamma
c     = alpha - I delta - beta + I gamma
cstar = alpha + I delta - beta - I gamma
aa = a^4 + astar^4
bb = b^4 + bstar^4
cc = c^4 + cstar^4
aap = a^4  astar^4
bbp = b^4  bstar^4
ccp = c^4  cstar^4
