You are a triangular based pyramid (tetahedron) with 4 faces, 6 edges and 4 vertices.
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triangle based pyramid
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.
pyramid
No. For example the triangles with sides {3, 4, 5} and {6, 8, 10} are similar but not congruent.