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How many faces, edges and vertices does a cube have? A cube has six faces, 12 edges and eight vertices. Each face of a cube is an identical square, and every edge has an identical length, which is equal to the length of the sides of the faces.
The prism shown below, which has an octagon as its base, does have ten faces, but the number of vertices here is sixteen. The pyramid, which has a 9-sided base, also has ten faces, but has ten vertices. But Euler's formula tells us that no simple polyhedron has exactly ten faces and seventeen vertices. Figure 6: Both these polyhedra have ten faces, but neither has seventeen vertices.