Now everyone from detectives to radio talk-show hosts is puzzling over the Dahmer case. The facts by themselves -- a home where parents went through a bitter divorce; a brother he long believed was the favorite in the family; a mother who he told the police had a nervous breakdown; his own lack of close friends -- do not explain why he did what he says he did. But the increasingly gruesome details that have emerged about Mr. Dahmer have all led back to one basic question: Who is this man?

He was an elementary-school student who stored animal skeletons in bottles of formaldehyde. A high-school drinker who swigged Scotch in early morning classes. An Army medic who convinced his buddies that he hated anything more unpleasant than taking soldiers' blood pressure. A factory worker who killed a gay man in a Milwaukee hotel, packed the body into a suitcase, took an elevator to the lobby, hailed a cab and had the driver put the suitcase in the trunk.

Like Mr. Gacy and Mr. Bundy, Mr. Dahmer went undetected for years. Some of his victims came from the fringes of society, and there were so many that he could not remember them all -- men he filed in his memory not by their names but by their tattoos. Some of them were like Mr. Dahmer himself, people of whom society did not take much notice. Disturbing Images From Childhood

And he could talk his way out of trouble when he had to. On May 27, nearly two months before his arrest, neighbors called the police about a naked, bleeding teen-ager they had seen wandering on the street outside Mr. Dahmer's apartment. The officers who investigated believed Mr. Dahmer's explanation that he and the boy were living together and were just having a quarrel.

After they left, Mr. Dahmer said later, he killed the teen-ager, Konerak Sinthasomphone. The officers have been suspended, with pay.

He had a glib side, talking his way into Vice President Walter F. Mondale's suite and the office of the humorist Art Buchwald on a school trip to Washington. But his hometown -- Bath Township, Ohio, a prosperous community that was home to Firestones and other decision makers who presided over the tire factories of nearby Akron -- was a tight-lipped place. Mr. Dahmer was tight-lipped about himself. And if anyone realized how unusual some of his behavior was, no one did anything about it.

"Whatever had gone on in Jeff's life, he couldn't talk about." said Martha Schmidt, a classmate at Revere High School who is now an assistant professor of sociology at Capital University in Columbus, Ohio. But she added, "It seemed so clear all along that it was someone saying, 'Pay attention to me.' "