Dodecahedron.
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A polyhedron is a solid figure with many plane faces, typically more than six.
A cube
There is no such figure.
A solid figure that has some of the same faces but some different faces, and has one more face than the other, is a prism and a pyramid. A prism has two identical bases and rectangular or square faces, while a pyramid has a polygonal base and triangular faces that meet at a single point, called the apex. The prism has one more face than the pyramid.
It's the adjective form of the word polyhedron, which means a solid figure with many plane faces, typically more than six.