Tetrahedron
That's called a cube.
A rectangle is a 2D object with four sides or edges, but does not have any faces. Only 3D objects have faces. A rectangular pyramid has six faces.
A tetrahedron, also called a pyramid is a three-dimensional shape with four faces.
A Heptagon is a 3d object with 7 faces. An example of a heptagon is a hexagonal pyramid (that is a pyramid with a hexagon for the base).
A cube is a three dimensional object with all faces squares. A cuboid is a three dimensional object with 4, or all 6, faces rectangles (and not square).
A pentagon is a 2 dimensional object. The 3 dimensional object, with 12 pentagonal faces, is called a dodecahedron.
[object Object]
As a 2d object, a diamond had four sides. As a 3d object, there are many different types of diamonds, all with their own numbers of vertices, edges and faces.
Cube
A pyramid
A quadrilateral is a plane or 2d figure with four sides. A 3d shape (object) has a name ending with -hedron, eg a tetrahedron which is a four sided 3d shape. A 3d quadrilateral has no meaning. Sides (edges) do exist in 3d shapes, but a more pertinent attribute is faces. Do you mean by "3d quadrilateral" a 3d shape which has a quadrilateral as a base and at most 4 or 5 other sides, ie a pentahedron (usually called a square pyramid) or a hexahedron (some types of which are called cuboids and cubes)? Please re-ask using consistent terminology, eg What is a 3d shape with one pair of parallel faces and 6 faces?
An object with 6 faces is called a hexahedron, more commonly known as a cuboid or cube (a regular cuboid).