A prism with an n-sided base will have 2n vertices, n + 2 faces, and 3n edges.
A pyramid with an n-sided base will have n + 1 vertices, n + 1 faces, and 2n edges.
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A Tetrahedral * * * * * It is a tetrahedron (tetrahedral is its adjective). And, in any case it IS a pyramid - with a triangular base.
A tetrahedral prism is a three-dimensional geometric shape that has two congruent triangular bases and four congruent lateral faces that are in the shape of triangles. The lateral faces connect the corresponding vertices of the two triangular bases, forming a solid with six faces, eight edges, and four vertices.
A tetrahedral die (not dice!) is a triangle-based pyramid, whose four faces are equilateral triangles.
"Tetrahedral" is an adjective. It needs a noun associated with it before it can be an abject that may have edges.