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The authors demonstrate through numerical simulation and experimental measurement that a polyplanar scan geometry consisting of a flat-topped pyramid provides a possible solution to the measurement of high-gain antenna patterns in the forward hemisphere using a planar scanner of size of order 1.5 times the size of the radiating aperture. The importance of correctly determining the normal field component for each partial scan data set is demonstrated and a new auxiliary rotation near-field to far-field transform algorithm is proposed. Additionally it is shown experimentally that by enclosing a medium-gain antenna (e.g. a corrugated horn) within a scan geometry formed by an imaginary box and measuring the near field on all six sides of the box using a suitable rotation of the AUT, a prediction of the full spherical radiation pattern of the antenna can be obtained.