An octahedron.
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You are a triangular based pyramid (tetahedron) with 4 faces, 6 edges and 4 vertices.
A cube always has six congruent faces and eight vertices.
The Platonic solid known as an octahedron would fit the given description
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 cube.