We prove that the spectrum of the variety of idempotent, right modular and anti- rectangular groupoids consists of all powers of four. We also prove that any nite or countable groupoid anti-isomorphic to a groupoid in that variety is isomorphic to it. Finally, it is proved that, to within isomorphism, there is only one countable groupoid in that variety and that it is isomorphic to a proper subgroupoid of itself.