any pyramid
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The solid figure that has the same number of faces and vertices and has 8 edges is a cube. A cube has 6 faces, 8 vertices, and 12 edges, so it fits the description given.
Any pyramid.
A cube and a regular octahedron have the same number of edges, vertices, and faces. Both have 12 edges, 8 vertices, and 6 faces.
A rectangular dipyramid.
Any polyhedron can be deformed (its angles changed) without affecting the number of edges, vertices or faces.