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A triangular pyramid has these characteristics. The regular triangular pyramid is one of the Platonic shapes.
Because a tetrahedron is a triangular based pyramid that has 4 identical faces and 4 faces meet at all the vertices.
A tetrahedron.
Regular: and there are only five of them. They are also knows as the platonic solids.
Yes, the Platonic solids (excluding the sphere which does not have vertices).