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 Question from Mohamad, a student: Draw a net for a rectangular prism? Last week when we were studying for our finals we came across a section about drawing nets I would really appreciate it if you gave me some help on it

A net is simply any collection of polygons P(1)...P(n) in the plane that corresponds to the faces F(1)...F(n) of a polyhedron (for each i, P(i) and F(i) must be the same shape and size); is connected; and is such that if two polygons P(i),P(j) share an edge, then so do F(i) and F(j). Thus, by adding more joined edges the net can be folded into a polyhedron. Alternatively, by cutting edges the polyhedron can be folded flat in the plane without coming apart.

There is no easy rule for finding nets; indeed it is a very difficult open problem to determine whether there always is a net. For simple polyhedra it is usually not too difficult and there are usually many ways to do it. For your rectangular prism, start by drawing one of the square ends; draw (for instance) the four rectangular faces joined to it; then put the last (square) face on. Make sure all the faces you join in the net will be joined in the polyhedron!

Good Hunting!
RD

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