A tile for a combustor dome of a gas turbine engine includes a tile body defining an upstream surface and an axially opposed downstream surface with at least one injection orifice defined through the tile body from the upstream surface to the downstream surface. The tile body extends in a radial direction from a radially inner surface to a radially outer surface. The radially inner and outer surfaces define circular arcs that are concentric with one another. The tile body extends circumferentially from a first end face to a second end face. The first end face follows a sigmoid profile and the second end face follows a sigmoid profile configured to interlock with the sigmoid profile of the first end face of another identical tile body.