6 of them.
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A tetrahedron is a triangular pyramid. It has six edges, four faces and four vertices.
tetrahedron
A tetrahedron has 4 vertices. By the way it has 4 faces and 6 edges.
A truncated Octahedron has 36 edges.
a sphere has no edgesOf the solids with planar faces and line edges the tetrahedron has the fewest edges and faces. (Four faces and six edges)