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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A cube has four space diagonals. One from each of the four vertices on the top face of the cube to the opposite vertex on the other face
A square has four edges, one face (assuming the "back" does not count), and four vertices. A cube has 12 edges, six faces (assuming the "inside" does not count), and eight vertices.
Four vertices Four equal sides Four equal angles
Four faces four vertices
5 vertices