A geometric net of a 3-dimensional object is a single two-dimensional figure that can be folded into the 3-d shape.
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A net is an unfolded 3D geometrical shape
We cannot assess the efficiency of a geometrical shape unless we have a particular purpose in mind. You will have to state what you wish to efficiently do, by means of a geometrical figure.
A geometrical straight line is infinite but if it has defined end points then it is a line segment.
A sphere
Parabola