Someone posted links to houses that had "California roofs", but I wasn't able to distinguish what makes them have the name. And now, calling them Eichler roofs is not clearing them up any further.
If the top is a foot wider than the bottom, what does that mean?
The description and appearance (aside from the center roofline in the image) really appear to fit the nature of the prairie house archetecture, with its deep eaves. In winter, the low sun provides a lot of heat and light to the interior, while in the summer, when the sun is high, the direct heating and lighting is minimized. Images here don't link to informative pages, but they show solar paneling being installed on a flat roof.
"Houses of the Prairie style are characterized by an overall horizontal emphasis achieved by low proportions, low-pitched or flat roofs with wide overhangs, banded casement windows, and low, massive chimneys. Prairie houses are irregular in plan, two stories high, with one-story wings. Siding is brick or stucco with stone or wood trim.
The Prairie style was developed in Chicago by architect Frank Lloyd Wright around the turn of the century. Wright disapproved of styles that were revivals of earlier styles and designed buildings with horizontal emphasis and an open simplicity that would relate to the flat, open landscape of the Middle West. The Prairie style is most common in Chicago, other parts of Illinois, and in surrounding states."
(The small descriptions of the Eichler boom seem to locate them in the SF Bay area.)