Answer to Question #350943 in Geometry for Mpho

Question #350943

Name a non-polyhedral and say why it cannot be a platonic solid


1
Expert's answer
2022-06-17T05:00:10-0400

A polyhedron is a three-dimensional solid made up of polygons. It has flat faces, straight edges, and vertices. For example, a cube, prism, or pyramid are polyhedrons. Cones, spheres, and cylinders are non-polyhedrons because their sides are not polygons and they have curved surfaces.




Theorem. There are exactly five Platonic solids. The key fact is that for a three-dimensional solid to close up and form a polyhedron, there must be less than 360° around each vertex. Otherwise, it either lies flat (if there is exactly 360°) or folds over on itself (if there is more than 360°).


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