Visualize "house," and your first mental image is likely to be a two-story, gable-ended shape much like the houses in the game of Monopoly.

Or your architectural memory might focus on special houses like the White House, the Octagon House (really a hexagon) or a chateau in France's Loire Valley. If you grew up in Texas or California, you may think of one-story ramblers with overhanging roofs shading picture windows and sliding glass doors.

The single-family detached house, standing free on its own piece of land, always has offered its owner, designer or builder the greatest flexibility in determining its size, shape and style. Consequently, types of detached houses seem limitless, ranging from manufactured homes to modest bungalows and Cape Cods to center-hall colonials to spacious villas and palaces.

Yet all houses, small or large, ancient or contemporary, generally contain two primary spatial zones: public rooms or areas where people arrive, circulate, gather, socialize or dine; and private spaces -- bedrooms and bathrooms -- where people sleep, bathe and perform other activities of a more personal nature. Service spaces for food preparation, storage and "machines" sometimes can form a third zone, although they often are integrated with the other two.

These zones can be organized vertically, usually with private spaces upstairs and public spaces downstairs. Collections of rooms assembled in this way may derive visual and functional unity from a central stair along with foyers and hallways linking individual rooms to the nonroom, central-stair space. Grand foyers and staircases are sometimes the most dramatic and memorable architectural events in such houses.

Another fundamental room-ordering system, also quite ancient, places rooms around an atrium or central courtyard that provides light, air and space for circulation and other activities. Pompeian villas and Italian Renaissance palazzos are well known historical prototypes for such houses.

In atrium houses, the zone of public rooms may be on the ground floor, surrounding the atrium, with private rooms above in upper stories. Or public and private rooms can be separated horizontally by the atrium, with public rooms on the streetfront side and private rooms on other sides. Sometimes, the atrium becomes an entry courtyard facing the street or a private garden court away from the street.

Houses can have "wings" containing one room or a zone of rooms that penetrate or embrace the landscape. Patterned like L's, U's, T's or I's, they can stretch, step and bend to fit the topography and geometry of their sites. Wings allow houses to expand, although mating new wings to old bodies can be a formidable design challenge. In the 16th century, the great Italian architect Andrea Palladio developed an extensive repertoire of house typologies embodying wings, courtyards and pavilions based on Roman prototypes. His designs, organized symmetrically about a centralizing room, court, porch or pavilion, have influenced the composition of stately houses ever since.

Three-part designs (central pavilion with two side wings) and five-part designs (central and end pavilions connected by two hyphen-like wings) typify many English and American houses of the colonial period. In today's neo-Palladian houses, such wings and pavilions probably accommodate automobiles, TV and stereo systems, or hot tubs.

A familiar and favorite strategy for shaping a single-family detached residence is to organize it on one level. Primitive house types -- tepees, African huts, Indian hogans, log cabins, igloos -- are one-story structures because of limited construction techniques, cultural tradition and convenience. Availability of land is also a factor; putting domestic activities on one level obviously requires more territory but less structural prowess than putting them on two or more levels.

Most one-story houses likewise separate zones of relative privacy and communality. Part of the house normally consists of a living room, dining room and kitchen, while the other part is dedicated to bedrooms, baths, narrow hallways and closets. Unless there's a basement or usable attic, no stair is required.

Early in this century, Americans discovered the bungalow, a house type imported from India. Akin in scale to the Cape Cod cottage (a derivative of English cottage architecture), the bungalow became popular because it was compact, economical and easy to construct. Although unpretentious in size and decoration, the bungalow typically had a front veranda that imparted graciousness and a hint of formality to an otherwise simple, one-story box with an attic.

Stretch a bungalow or Cape Cod cottage and you get a rambler or ranch-style house. These became "de rigueur" in the American Sun Belt, where land was plentiful, lots were big and the climate was hospitable most of the year. Conserving heat in winter by stacking public and private floors between a basement and attic, inside a relatively compact envelope, seemed unnecessary.

The "prairie" houses of Frank Lloyd Wright furthered the popularity of these low-rise American house types. Stressing the earth-hugging horizontal with cantilevering roofs floating over walls of windows, Wright's houses often were organized geometrically around a primary vertical object -- most notably the fireplace and chimney -- rather than around a singular space or room. In contrast to houses whose figural centers were stair halls or courtyards, Wright-inspired homes contained interlocked spaces that radiated outwardly from the solid, central hearth.

After the 1920s, international-style houses -- designed by architects such as Richard Neutra, Walter Gropius, Marcel Breuer and Mies van der Rohe -- caught the public's attention with their open, "free" plans. Wright had pioneered the use of fluid, horizontal space focused centrifugally on the landscape as an alternative to inwardly focused, rigidly defined rooms. But later modernists went even further, sometimes eliminating totally any vestige of a spatial or sculptural "center." Rooms and activities merged in a space "continuum" that, in turn, merged visually with the outdoors through glassy walls.

Many houses built in America during the last half century clearly show the effects of these modern design ideas. Living and dining rooms became one space. The family room was invented, often flowing into the kitchen, which, in turn, might flow into the dining area. Instead of front porches of consequence, side and back porches grew larger. Backyard patios and decks further extended the public living zone via sliding glass doors.

Following World War II, the suburban split-level house arrived. These hybrid houses indeed are split vertically into two wings offset from each other by a half-story. An entry foyer and scissor stair lead up and down half levels to public or private zones. This configuration, well suited to sloping lots, readily produces cathedral ceilings and walk-out basements.

Despite "modern" spatial gestures found in new generations of house types, builders rarely abandoned completely the historical imagery of previous centuries. Vestigial classical columns and porticoes, cornices and decorative trim still are tacked on to otherwise contemporary house forms to increase their market acceptance. Even manufactured housing, perhaps assembled partly by robots, can be given traditional styling.

Look closely at single-family detached houses you inhabit or visit. No matter how they are decorated, their antecedents, typologically speaking, may not be what you thought they were.

NEXT: The factory-built house.