It is the cube of the ratio of lengths of their edges.
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No, the ratio of the volumes of two similar solid polyhedra is equal to the cube of the ratio between their edges. The volume of a solid object is proportional to the cube of its linear dimensions, not the square root.
No, because a polyhedron is a solid with many flat faces. A heptagon is not a 3-D figure. However, a pyramid or prism would be a polyhedron.
A polyhedron is in a subclass of geometric solids. The difference is that a polyhedron must have flat faces and straight edges.
A Platonic solid?
A pyramid, as well as any other solid figure bounded by plane polygons or faces, is a polyhedron.