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Polytope rope

Polytope rope

Today we are going to do a craft in class. It is about joining all the points of a polytope with ropes to make a very beautiful picture like the one in the drawing. The circumference has 20 points marked in red so that each of the points joins each and every one of the rest of the points with a rope between them so that we have a section of rope between any two points.

Do you know how many stretches of rope I need to make my polytope?

Solution

The figure has 20 points and there has to be a connection with each of the remaining 19 points which would make a total of 20 * 19 = 380 sections but since each one is shared by two points, we actually have half, that is , 190 sections of rope.

If you are curious you can see other polytopes on Wikipedia and you will find images of some already built on this page.