Fender Bass VI
This is a fairly rare bird. From 1962 to the early '70's less than 7-800 were made. It is a six string guitar, but tuned a full octave lower than standard tuning. This means that the low E string is the same pitch as the low E of a bass guitar. A Bass 6 neck is in between an electric guitar and an electric bass guitar in length. These qualities make it truly a jack of all trades and master of none. The Cure use them because when you play high up on the neck, it is the same pitch as the lower notes on a guitar, but the tone and timbre of the sound is quite different. The lightest string on a Bass VI is .025", and is wound stainless steel over a steel core, while the thinnest string on a guitar is .010" or so, and is plain steel wire. This makes the tone of the two very different.
For an example, listen to Spiderman off of Disintegration The electric guitar only plays the off-beat chords, while the melody is played (by Smith) on a Bass VI. The result is a much spookier sound than provided by a guitar.