solid with 1 edge is a cone .
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an edge or in more simpler term "side"
edge
A face.
An edge is a straight line as part of a polygon. It can also be the straight line joining two faces of a solid which has polygonal faces.
The Name Platonic solid Comes from Plato the second main reseacher of the five solids. Pythagoras was the one discovered the platonic solids