pyramid
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A pyramid fits the given description
The 7-letter word for a 3D shape with triangular faces is "pyramid." A pyramid is a polyhedron with a polygonal base and triangular faces that meet at a common vertex called the apex. Pyramids are classified based on the shape of their base, such as square pyramids, triangular pyramids, pentagonal pyramids, etc.
The given description fits that of a triangular based pyramid which has 4 faces, 6 edges and 4 vertices
A vertex can be the corner of a polyhedron in which case at least three edges meet at a vertex.
An endpoint where two edges intersect on a polyhedron is called a vertex.