No. I has 3 triangle faces and one square face.
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trianglesbecause TRIangular prism pyramid means that TRIangles are the bases, which also mean the faces.
A triangular pyramid has four faces, and is referred to as a tetrahedron if the faces ale all equilateral triangles.
A 3D shape with all triangular faces can be a tetrahedron pyramid.
That sounds like a square-based pyramid.
There are infinitely many polyhedra all of whose faces are triangular.