There is no such shape.
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6 flat surfaces - known as faces, 12 edges 8 vertices.
A triangular based pyramid has 4 flat faces, 6 edges and 4 vertices.
A triangular based pyramid would fit the given description.
a cube
A cube or cuboid have 6 flat surfaces and 8 vertices. (A cuboid means shaped like a cube - an example being a shoe box.)