triangle based pyramid
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square based pyramid
You are a triangular based pyramid (tetahedron) with 4 faces, 6 edges and 4 vertices.
An icosahedron.
An octahedron.
A four faced figure is a tetrahedron. If they are all congruent triangles, they are all equilateral triangles and it is a regular tetrahedron - one of the 5 Platonic Solids.