A ceiling system is provided for use in a building space having a plurality of walls. The ceiling system includes a grid system that extends to at least two of the plurality of walls and separates the building space into an occupiable space below the grid system and a plenum space above the grid system; and a plurality of ceiling tiles that are supported by the grid system and, with the grid system, create a barrier between the occupiable space and the plenum space, the plurality of ceiling tiles including three different polygonal non-rectangular ceiling tiles.