A triangular bipryramid (two triangular pyramids stuck together on one face), a parallelepiped (like a squished cuboid), a pentagonal pyramid.
A cube or rectangular prism are special cases of a parallelepiped.
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There are infinitely many shapes that do.
Such a shape does not exits. See the attached link for all 3d shapes with 6 plane faces.
Polyhedra (singular = polyhedron).
triangular pyramid and cube.
6 faces, 12 edges