A 'unit cube'. Just like a circle with radius 1 and center at (0,0) is a 'unit circle'.
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There are twelve edges on a cube. If you mean the vertices (the corners), then there are 8.
A Fladoodle. Eg, one icecube=1 Fladoodle
It is a term that is not properly defined. It could, most likely, refer to a line that is 1 unit long, or a square that is 1 unit*1 unit, or a cube of sides 1 unit, or indeed a hypercube in higher dimensions The unit in question would normally be a standard measure of length such as a centimetre, metre, kilometre, inch, foot, mile, light year, parsec. But, equally, it could be the length of the little finger on your right hand!
it depends on the shape. the unit should be given
There is no conversion between square yards and yards, because the units refer to different things. "Square yards" is a unit of area, while "yards" is a unit of length. But there is a relationship. Taking the square root of the units of square yards will give you the measure of the side of a square whose area is equal to that number of square yards. For example, an area of 4 square yards can be represented by a square whose sides each measure 2 yards, 2 being the square root of 4.