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A non polyhedron does not have these properties, maybe it is not closed, maybe one or more of the sides is a curved surface. In some branches of topology the sides of a polyhedron cannot intersect each other.
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What is a polyhedron with no bases?
A non polyhedron with 0 bases is a sphere.
What is non-polyhedron?
A polyhedron has "many sides" (by definiton). The only 3-D shape which does not have "many sides" is a sphere (which technically only have one "side").
What is a non polyhedron with 2 congruent and parallel bases?
A cylinder is one example.
The edge of a polyhedron are the polygons which bound the polyhedron?
No, they are the faces of the polyhedron.
What is a non polyhedron with 2 parallel bases that are congruent?
It is a prism with non-polygonal bases. The bases simply be two identically shaped "blobby" shapes.
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