A flat narrow fold in cloth is called a pleat. Pleats are created by folding material over on itself and then securing it in place with stitching or pressing. They are often used in clothing and home décor to add structure and design detail.
a pleat
Sounds like a pleat.
flat felt seam
It is known as the hem. A hem is a stitched narrow fold of cloth that prevents unravelling of a raw edge.
i have narrow flat curved stool
A fold is when an object, normally a flat and thin one, is bent and part of the object placed on top of the rest of it. You can fold paper, cloth, omelets, sheet metal, carpets, etc. etc. In topography, a fold is a gentle curve of the ground; a slight hill or hollow.
not completely flat, but they do fold down
A seam
Wash it and fold it leaving it there for about 4 weeks
a flat pack mountain
GMC acadia