This is the "Shmoo", a fore-runner of the Trimline
This telephone was used in field trials between 1959 and 1960 in New Brunswick, NJ. (Info thanks to paul-f.com)
The nickname for this telephone was a reference to The Shmoo, a character in the Lil' Abner comic strip, who the handset of this phone coincidentally resembles.
A close-up of the dial portion of the handset. Notice the space between the 1 and the finger-stop, the smaller dial with the moving finger-stop used in later Trimline phones had not yet been developed, causing this telephone to have this distinctive bulging shape. The screw-tab accesses the night-light.
A view from the top of the phone, showing more detail of the base. The base was designed to be used on a desk or wall-mounted.
What the Shmoo looked like when its handset was in the base. In this view you can see the phone's night light switch.
Another view of the phone on its base, from the handset cord end. The base had approximately the same footprint as a Princess phone, 3 1/2 x 8.
A close-up of the phone snuggled in its base. From this angle, it looks a lot like a wireless computer mouse in its charging base. This was, of course, about forty years before those were invented.
The phone's underside, showing its Western Electric field trial model number.
While participants liked this dial-in-the-handset style, tests concluded the bulging shape was too uncomfortable to hold for long periods of time.