Players at the Ivy League school in upstate New York, live in a 14-room house they lovingly call the Dog Pound. And the Big Red have won two games in the NCAA Tournament, with the hope of cutting down the nets in Indianapolis in two weeks as national champion.

Conventional wisdom holds that it should all come to an end Thursday night in Syracuse, N.Y., where the No. 12 seeded Big Red run into No. 1 seed Kentucky in an East Regional semifinal game.

That same wisdom, however, had coach Steve Donahue’s team losing to Temple in the first round last week in Jacksonville, and to Wisconsin in the second round. Didn’t happen, not even close. The Big Red beat Temple by 13 points and Wisconsin by 18, improving their record to 29-4 and leaving a team with four senior starters thinking it has the ability to do just about anything it wants.

“We’re just getting started,’’ said 7-foot center Jeff Foote, who was no more than a marginal Division 3 prospect who started his collegiate career as a walk-on at St. Bonaventure. But he filled out and has become one of the anchors of a team that has won 72 games over the past three years, including three consecutive Ivy League titles (and three straight NCAA berths). “We have a really special team and we’re capable of a special run,’’ he said.

The wins bonded the team; 13 players and a manager live in a house five minutes from campus, which drew the attention of the team when it saw an ad in the paper that said, “Big Ugly House for Rent.’’ “We looked at it as a sign,’’ said Foote, who along with 6-7 senior Ryan Wittman and 5-11 senior Louis Dale are the cornerstones of Cornell’s success.

Wittman’s father, Randy, was a member of the Indiana team that won the 1981 national championship and was also coach of the Minnesota Timberwolves.

Foote was pushed to Cornell by his mother, Wanda, who was an emergency room nurse and liked the Big Red coaches when an accident brought a Cornell player, Khaliq Grant, who had been temporarily paralyzed during practice, to the emergency room of the medical center in Elmira, N.Y., where Foote’s mother was on duty.

Wanda Foote became friendly with the Cornell assistants and told them about her son, who went to Donahue and told him about Foote. Donahue, who has been coaching at Cornell for 10 years and is sure to be on the short list of schools looking for new coaches (Seton Hall?) endured six straight losing seasons before the class led by Foote, Wittman, and Dale turned the Big Red into the new powerhouse in the Ivy League.

Foote is one of Donahue’s favorite success stories. “I love talking about this because it’s a lesson for me as a coach,’’ said Donahue. “I was sitting with a couple of Division 3 guys and [Foote] is probably 6-10, 170 with a shaved head. It was hard to imagine him being a college basketball player at any level. None of those Division 3 coaches were willing to give him a look. You see so many big kids, you always hope that maybe one has a chance and you take a flier on him.’’

Part of the formula for success has been the off-court bonding. “I love all these guys,’’ said Foote. “We’re all like brothers.’’

It is an eclectic group, starters to subs, with different personalities. Although all the veterans have a 3.0 or better grade-point average, freshman forward Eitan Chemerinski, who came to Cornell from Potomac, Md., via the Charles E. Smith Jewish Day School, is regarded as the brain of the group.

“I don’t know if you guys saw him do the Rubik’s Cube in about 2 1/2 minutes,’’ said Wittman. “I don’t know if all of us could pull that off.’’

On the court, Cornell is pretty astute as well, especially when all five starters shoot better than 42 percent from the field and the team leads the country in 3-point shooting percentage.

The Big Red simply outshot the Badgers. “It’s tough when you shoot 52 percent in the first half and you’re still down by 12,’’ said Wisconsin coach Bo Ryan. “They can beat you in so many ways.’’

Cornell, which became the first Ivy League team since 1998 to win an NCAA Tournament game, respects Kentucky but is not intimidated. “You know, watching Kentucky on TV, they’re a great team,’’ said Dale, the point guard from Birmingham, Ala., who was lightly recruited and who scored 26 points against Wisconsin. “You can tell that from the beginning. They like to push it and we just want to stay within ourselves and do what we can and do the things that we can control.

“We’ve got eight seniors on this team and we want to take this ride as long as we can because after this it’s just babies and memories, so we’ll just keep going.’’

Just how far Cornell can go is one of the intriguing questions remaining in a tournament that already has produced more than its share of great stories, with the success of No. 10 seed Saint Mary’s, which upset No. 2 seed Villanova in a South Regional second-round game, and No. 9 seeded Northern Iowa, which stunned No. 1 seed Kansas in a second-round Midwest Regional game.

“Obviously we have a lot of seniors on our team,’’ said Wittman. “And I think that is something that motivated us. Not only throughout the season, but in the offseason, just knowing that this was our last shot to come here and make some noise and win some games.’’

Mark Blaudschun can be reached at blaudschun@globe.com.