For me, this is possibly the best head that Gillette ever made. Note the flat-bottomed baseplate. You can find this style of baseplate on some, but not all, Big Fellow and Criterion razors, as well as some of the Bostonians.
However, with those older style razors, the baseplate is attached to the handle.
This ’New Deluxe’ razors are also 3 pieces, but the head, top-cap and handle are 3 seperate pieces. This one hails from the 1930s.