The alternating-plane property identifies the roots of a complex polynomial obtained by factorising the denominator of even-degree magnitude-squared transmission-coefficient functions with even-numerator polynomials and reflection zeros constrained to occur in single conjugate pairs at real frequencies in the pass-band. The transfer functions considered in this paper are realisable by Rhodes's physically symmetrical prototype network, and a practical application of the alternating-plane property is to simplify the construction of the admittance function required for the synthesis of the prototype network.