Futons can have bifold frames, loveseat frames or trifold frames. Bifold frames are the most common; these are the type where the mattress folds in half to convert the futon bed to a couch. Bifold frames usually come in full and queen sizes.
Loveseat futons are space saver futons that are slightly smaller than bifold futons and are usually chosen to fit in smaller spaces. They hold two-piece mattresses and come in twin and full sizes. Trifold futons fold the mattress in thirds; because of this, only very thin mattresses can be used on them. Trifold futons are usually difficult to convert from bed to couch and back.