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A relatively simple method is presented for calculating the impedance properties of antenna arrays consisting of n identical radiators oriented at the vertices of regular polygons. All antennas are required to carry currents of equal magnitude, but not necessarily of the same phase. However, the choice of phase angle must be such that the required electrical symmetry of the array is unimpaired. The case of a circular array with a central radiator is discussed. Immediate practical applications of the theory include: (a) Determination of the driving-point impedance of the primary radiator in a corner-reflector antenna. (b) Calculation of the power lost through radiation, or conversely the signal pickup, of certain multiple-wire transmission lines, when operated in a resonant condition. (c) Analyses of problems involving symmetrically disposed fixed antennas for direction-finding purposes. (d) Ascertaining the effectiveness of circular arrays for transmission. Several numerical illustrations of the theory are given.