A small, faint, relatively cool star is called a red dwarf.

Here's why:

* Small: Red dwarfs are the smallest and least massive stars on the main sequence.

* Faint: They are much fainter than our Sun, emitting far less light and heat.

* Cool: They have the lowest surface temperatures of all star types, hence the "red" in their name.

While "red dwarf" is the most common term, you might also hear them referred to as M-dwarfs because they belong to the M spectral class.