Special complex variables techniques are used to obtain the six flexure functions (one of which is the torsion function) of a certain isotropic cylinder under flexure. The cross section is bounded by the closed curver=a sin4(θ/4) (−π<θ⩽π). The torsional rigidity, moment integrals, and the associated twist are also evaluated for this beam. It is worthy to mention that these techniques work successfully when they are applied to any of the cross sections bounded byr=a∥sin(θ/n)∥ n ·(−π<θ⩽π), wheren is a positive integer (n>1).