A cantellated regular tetrahedron, in the form of a regular cuboctahedron, has
14 faces (8 triangular, and 6 square), 24 edges and 12 vertices.
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A tetrahedron has:4 faces4 vertices6 edges
A tetrahedron which is a triangular based pyramid has 4 vertices, 4 faces and 6 edges
A triangular based pyramid which is a tetrahedron has 4 faces, 6 edges and 4 vertices
A tetrahedron triangular based pyramid has 6 edges, 4 faces and 4 vertices
Assuming that a solid triangle is a tetrahedron, the answer is: faces: 4 edges: 6 vertices: 4