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Its base has 2 pairs of opposite parallel edges and it has 5 faces, 8 edges and 5 vertices.
A triangular-based pyramid, also called a tetrahedron, has no parallel faces, but has 4 faces, 6 edges and 4 vertices
Two pairs
Only the base can have parallel edges since all other faces are triangular. So, at most one face.
There are 257 topologically different convex octahedra. Many of these will have no parallel faces. It can have four pairs of parallel faces.