Three things:
Cotton
Pencil
Diamond
What do they all have in common?
I think the answer to the question is
Carbon.
Cotton:
Cotton is a biological substance, and thus carbon based.
Pencil:
The pencil lead is made of graphite, which is carbon.
Diamond:
A diamond is just another form of carbon.
Another possibility in addition to the other two answers
Their hardness (or softness) is desired or otherwise significant
cotton
Many people want cotton to be as soft as possible, even using thread count as a rough measure of softness of cotton sheets
pencil
Artists, drafters, and other people use pencils of varying hardness
diamond
diamond defines 10, the highest hardness, on the Mohs scale
They all involve:
Carbon
Cotton
Cellulose fibers (Plant made from carbon)
Pencil
Graphite in the lead (Carbon is soft graphite)
Diamond
Diamonds are compressed carbon
Or
They are all ways to describe clothing
(Do a google search on "Cotton Pencil Diamond" & you'll see what I mean)
Cotton Blend Diamond Print Pencil Skirt