As for models of π Speakers, there are three basic types.

The one π and two π speakers have a direct radiating cone woofer and dome tweeter. The tweeter is designed with a wide surround and is capable of relatively high excursion, making a first-order crossover possible. The woofer becomes increasingly directional as frequency goes up, but the crossover range is very wide because of the use of a first-order crossover. So there isn't an abrupt change in directionality due to the fact that the woofer and tweeter share a wide common band.

Three π and four π loudspeakers use DI matching between the cone woofer and horn loaded tweeter. Crossover is done where the woofer directionality narrows to match that of the horn tweeter. This prevents a sudden change in in directionality because the woofer and tweeter are about the same at the crossover point.

The five, six and seven π loudspeakers use the room's corner to confine woofer radiation to the 90° wall angle. This is matched by the midrange and tweeter directionality, since both also use 90° flares.