Well...5x12 = 60, and the factors of 60 are 1,2,3,4,5,6,10,12,15,20,30 and 60...so I'm thinking only 3x30, 4x15, 5x12 and 6x10? (As all numbers have to be => 3 to fit the shapes in.)

Well it would be 3x20 (not 3x30) but even so not all those rectangle dimensions are possible to form.
 
Aye your method was interesting. Good point regarding the 1x1x1 description too.

Still thinking. :)

EDIT: It's not like...
...dry white wine or something is it?
ANOTHER EDIT:
It must be a towel, or a sponge. :)

Well...5x12 = 60, and the factors of 60 are 1,2,3,4,5,6,10,12,15,20,30 and 60...so I'm thinking only 3x30, 4x15, 5x12 and 6x10? (As all numbers have to be => 3 to fit the shapes in.)

Its a towel.
 
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