The number of vertices and faces is 2 more than the number of Edges according to Euler's formula. So a gemstone with 22 edges must have a total of 24 faces and vertices.
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A polyhedron satisfies the Euler Criterion which requires you to know two of the three - vertices, edges, faces - before you can determine the third element.
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2 faces, 4 edges, and 4 vertices 2 faces, 4 edges, and 4 vertices
Vertices: 12 Edges: 30 Faces: 20
8 faces, 12 edges, 6 vertices
It has 14 faces, 24 edges and 12 vertices