Dihedral evaluations of hypergeometric functions with the Kleinian projective monodromy

Algebraic hypergeometric functions can be compactly expressed as radical or dihedral functions on pull-back curves where the monodromy group is much simpler. This article considers the classical 3F2-functions with the projective monodromy group PSL(2,F7) and their pull-back transformations of degree 21 that reduce the projective monodromy to the dihedral group D4 of 8 elements.