It is a tough, unnerving problem, one to which architects, along with just about everybody else in America, have paid small attention: How to provide a dignified space for an individual who is a part of the country's most dispossessed and most diverse minority -- for a person who is, literally, homeless?

This is a question that could, and doubtless should, engage the nation's greatest minds. At present, however, it engages most deeply the talents of five advanced architecture students from the City College of New York and two of their professors.

With the help of an emergency $17,500 grant from the National Endowment for the Arts, this little band has been wrestling with the bricks-and-mortar issues for several weeks in a bare-bones studio at the sprawling, makeshift shelter for homeless persons at 425 Second St. NW, the one that Mitch Snyder almost died in a hunger strike to establish and that President Reagan, contacted on Air Force One in the final days of last fall's campaign, agreed to support.

The Second Street shelter, in the words of Reagan's secretary of health and human services, is to be made into "a model physical shelter to house the homeless in the District of Columbia." The imposing -- some would say impossible -- job, in Snyder's words, "will be done before next winter. The government's got the resources to do it and it will be done."

The most memorable thing about this huge shelter, as it is now, is not the pervasive smell of urine in dark halls and fetid dormitories, nor the broken doors and windows and holes punched viciously in plasterboard partitions, nor the despoiled carpets and the aging, putrescent green of hallway walls, nor the leaking roofs and motley hand-me-down furniture, nor even the almost insufferable sense of human vacancy and social derangement in the vast, ill-lit cavern (called the Drop-In Center), where street people and others near the end of the line congregate -- way too civilized a word -- during the day, when the beds upstairs are empty.

Far more memorable is the gut-wrenching poignancy of places people make for themselves in mean circumstances. People whose lives seem definitively unrooted will leave their cots neatly made each morning, will select the most colorful blanket from what is offered, will carry in a plastic potted plant from some downtown alley, will cover a strip of wall with pictures cut from magazines, will place a book precisely in the center of a pillow, will wait for weeks for a corner location or rare single-cot room to be vacated, then pounce upon it and demarcate there a place . . . a small piece of semiprivacy, a tiny homelike island in a rootless, dirty, messy sea.

Of course, the reverse is also true, but for every ill-made bed, every rubbishlike pile of possessions, every floor strewn with stuff, every sign of collapse, insensitivity and brutishness, there are these signals, at once pathetic and uplifting, of strong personal needs being satisfied with whatever is at hand. It is perhaps ironic, but this shelter, because of its size and disheartening distance from "normal" lives, demonstrates better than the greatest mansion or tidiest house the profound extent, in our society, of the human need for shelter -- not physical shelter, simply, but also for basic, personal, differentiated space.

Snyder, a radical Christian, political activist and the public conscience of the Community for Creative Non-Violence, the communal organization that runs the shelter, has made this need the basis of the program for its architectural reconstruction.

"If the guests," he says, "feel that this is their house, if we can make them feel secure and at home as close as possible within the limits of this structure, then the odds are they will want to take care of the place, to respect it." The odds are, he also believes, that if the homeless "are given dignity and provided with social and medical services, then maybe they will begin to get some hope back, and they will want to get out of here."

This is the theory. It has been up to the CCNY students and their teachers to figure out how to provide the physical tools that will enable CCNV staff persons (some of them graduates of homelessness) and the guests to put the theory into practice. The students have been in Washington for three weeks. The professors have joined them at least once each week.

Their names are Sergio Ghiano, Helen Chung, Daniel Kamel, Domenick Schinco and Cecilia Lopez, students, and professors Alan Feigenberg and Conrad Levenson of the City College Architectural Center, a full-credit community design facility that is part of the CCNY architecture school. Levenson, who also heads a private architectural firm that specializes in moderate-, low- and, as is the case here, lower-than-low-income housing, is long acquainted with Snyder and suggested using the students.

"The first thing we asked Mitch," Ghiano recounts, "is, 'Can you describe a typical homeless person?' He said there is no such thing. The diversity is great. Some are violent, some aren't. Some are insane, some are perfectly sane. Some are old. Some are young. We have to try to meet all of these needs. In a way, we had to create a typical homeless person" in order to make what has to be a standardized design.

"The basic challenge," Levenson observes, "is to design spaces that respect an individual's territory and the individual rights of residents, and that also respond to the collective requirements and responsibilities."

"The security issue all by itself is complicated," Feigenberg adds. "There is crime safety, which means there is a need for surveillance. There is safety outside and safety inside. Access must be limited and doors kept closed. There is fire safety, which means clarity of plan and access to exits. There is safety for the women, who must be kept separated from the men."

Another major challenge is to make a place with some of the crucial, basic aspects of home -- privacy, security, light -- that is, all the same, a temporary facility. "I don't know whether we can do exactly what Mitch wants," says Schinco. "People might not want to leave."

"We don't like large shelters," Snyder says. "Community-based shelters are obviously better. But the small shelters can't house a commercial kitchen, they can't meet all of the needs. It's the hub-and-spokes idea. The facilities of this shelter can be used by the smaller ones."

Then, too, the resources, even when backed by the prestige of a president, are hardly limitless. Whatever the architects design must be attractive, durable and, basically, cheap. The idea, Levenson says, is to come up with a flexible design, "a concept of a shelter," that can be adapted for use in many other cities.

As developed so far, the concept is to provide, on the basement level of the three-story structure, separate drop-in centers for women and men with entrances at opposite ends of the building, offices for counseling and other services (such as clothing distribution centers), a medical center, a laundry and that big kitchen. (At present meals are cooked elsewhere, and often arrive cold.)

The residential spaces are to be divided into four separate "villages," each serving nearly 200 men, another to serve approximately 150 women, and another where 75 rotating staff members will sleep. Each of the guest centers will contain, in addition to places to sleep, an enclosed dining and lounge area, bathrooms and a "quiet room" where guests can relax, read and write.

Rather than long, dormitory-like rows of cots, the sleeping areas will consist of interlocking doorless cubicles with six-foot-high partition walls ("to lighten up this dark hole," Ghiano says), each measuring 6 by 7 feet (at 42 square feet precisely 3 square feet less than the minimum space established for displaced persons in Europe after World War II), and each with a standard 30-by-75-inch cotlike bed raised high enough to allow a standard footlocker to be stored underneath. There will be reading lights and, at Snyder's insistence, electrical outlets for radios or television.

The design throughout is both ingenious and straightforward. Three weeks of work have produced, in the accurate judgment of one of the teachers, "professional-level results, not student-level results." When Snyder concluded his initial review, he said, "I'll take two."

In the Cityscape column on recent architectural happenings in Takoma Park, Md., Marc LaPierre was credited with designing the new town clock. This he did. LaPierre Associates, his Washington landscape architecture firm, also was contracted by the city to plan, design and implement all the streetscape improvements in "Takoma Old Town."