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Six edges.
A triangular pyramid consists of a triangular base. Attached to each side of the triangular base is a triangular face and these all meet up at the apex of the pyramid. There are, therefore, 6 edges, 4 bases and 4 vertices.
A triangular based pyramid has 4 facxes, 4 vertices and 6 edges
A triangular based pyramid has 4 vertices, 6 edges and 4 faces
A triangular pyramid has 4 faces and has 6 edges