Hi

The exotic, complex f orbital shapes are rarely shown in textbooks. General (and organic) chemistry traditionally focuses on the lighter elements, but the f orbitals 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.

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.
	The 4fz3 - 3zr2 orbital corresponds to n=4, =3, and m=0. Two lobes point along the z-axis, with two bowl-shaped rings above and below the xy plane. The nodal surfaces are the xy plane and a conical surface passing through the nucleus and between the rings and the lobes.
	The 4f5xz2 - xr2 corresponds to n=4, =3, and m=+1. Six lobes point to the corners of a regular hexagon in the xz plane, with one pair of lobes along the y-axis. The three nodal planes pass between the lobes and intersect at the x axis.
	The 4fzx2 - zy2 orbital corresponds to n=4, =3, and m=+2. It has the same shape as the 4fxyz orbital, but the corners of the cube are in the planes defined by the x, y, and z axes and the three nodal planes cut between the lobes and intersect along the z axis.
	The 4fx3 - 3xy2 orbital corresponds to n=4, =3, and m=+3. It is identical to the orbital with m_=-3 except that a lobe lies along the y axis instead of along the x axis.