The exotic, complex f orbital shapes are rarely shown in textbooks. General (and organic) chemistry traditionally focuses on the lighter elements, but the forbitals aren't occupied in the ground state until element 58 (cerium). Even for elements beyond cerium, the f orbitals are deeply buried beneath the valence shell and they rarely play an important role in chemical change or bonding. However, the orbital shapes can be useful in interpreting spectra and in understanding the structure of some complexes that involve the rare earth elements. So here they are, if you need them.

The yellow and blue colors designate lobes with positive and negative amplitudes, respectively.

The 4fy3 - 3x2y orbital corresponds to n=4, =3, and m=-3. Six lobes point to the corners of a regular hexagon in the xy plane, with one pair of lobes along the x-axis. Three nodal planes pass between the lobes and intersect at the z axis.

The 4fxyz orbital corresponds to n=4, =3, and m=-2. Eight lobes point to the corners of a cube, with four lobes above and four lobes below the xy plane. The x and y axes pass through the centers of four of the cube's faces (between the lobes). The three nodal planes are defined by the x, y, and z axes.

The 4f5yz2 - yr2 orbital corresponds to n=4, =3, and m=-1. Six lobes point to the corners of a regular hexagon in the yz plane, with one pair of lobes along the x-axis. The three nodal planes pass between the lobes and intersect at the y axis.