There is no shape with only four triangular faces and five vertices. If there is also a quadrilateral face then it is a quadrialteral based pyramid.
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Yes.
A square pyramid has a square base and four triangular sides. This gives it five faces, eight edges and five vertices.
A tetrahedron, otherwise known as a triangular pyramid, has four faces, four vertices and six edges.
No. A triangular prism has six vertices. A square pyramid has five vertices. A triangular pyramid has four vertices.
A tetrahedron or triangular-based pyramid has four faces, six edges, and four vertices.