Art teachers have proposed various schemes for simplifying the head into an arrangement of flat planes. Here are two plane breakdowns by Andrew Loomis, author of Figure Drawing for All It's Worth and Drawing the Head and Hands.
The one on the left is a simple breakdown, with front, side, and bottom planes. The one on the right subdivides the planes further. To be precise, some of these "planes" aren't perfect planes in the geometric sense, such as the curving planes on the top of the cranium.
Fred Fixler, a student of famed Art Students League instructor Frank Reilly, came up with a slightly different plane breakdown for an idealized male head. There are some rounded forms too. The cranium is a ball with the sides sliced off.
Sculpting the plane head brings the plane analysis into the realm of reality. This one is by painter and teacher John Asaro, who has a website called "Planes of the Head." He has taught head painting using his plane head.
Many academic instructors have used plane heads as models before going to the live human, because it's much easier to accurately judge the values and color notes of each plane, compared to the infinitely variegated tones and curving forms of a real face.
Drawing and painting from plane heads is a central part of Chinese and Russian academic practice, and various companies have resurrected some of these art school models, such as this 21-Inch plaster head.
This mini plaster head is very different from a European or American standard head, and the planes are broken down into a mosaic of small forms. But the ear is treated as a single plane.
People will debate the merits of these commercially available heads, but I've never been completely satisfied with any of them. I think it's a great exercise for any student to come up with their own analysis, and that's what I did when I was in art school. Before I knew about Sculpey, I made this the hard way, sculpting a plastilina original, and then making a two-piece mold and casting it in plaster. Mine was inspired mainly by Loomis and George Bridgman.
I have set up my little plane head and painted him in colored light.
Once a student has had practice drawing and painting from idealized plane heads, and even sculpting their own breakdowns, then I think the next best step is to look at real human models and break the planes down in a unique way for that individual model.
This was the method taught in a seminar I took from Art Center instructor Paul Souza, and here's an exercise I did in that class, scumbling white oil paint over chip board sealed with shellac.
In truth, there is no single ideal plane head, and even an individual model's face can be analyzed in various ways.