Stranger Suns by George Zebrowski. Your description of the cover points to this edition.
This is from the back cover blurb, as quoted in a customer review at amazon.com:
Under the frozen ground of Antarctica lies the fantastic starship of a forgotten culture. Long dormant, it requires only passengers to awaken it . . . and Obrion's exploration team triggers the ship's launch. Prisoners in the empty craft, the four scientists find themselves reluctant, awestruck travelers through a universe where humankind has never ventured. And that is only the beginning: as Obrion and his companions explore the alien ship, they discover portals to an infinite number of variant Earths. The questions raised by these doorways are as innumerable as the worlds they access . . . but they only matter if Juan, Lena, Malachi, and Magnus can find their way back home.
And here is the discovery of the "duplicator cubbies". Lacking a copy of the book, I quote from the version in Amazing Stories, January 1991 (available at the Internet Archive) which may differ from the book version:
Magnus and the others stood before the wall of square cubbyholes, staring in silence. "This one here," he said.
Juan peered in. A bloody hand lay inside.
"As if freshly cut from my arm," Magnus said. "I put my hand in. The chamber glowed like the portals and there it was, down to the dirt under my fingernails. The principle seems an extension of the fluid doorways—direct manipulation of matter at the most basic level."
"Yummy," Lena said. "We'll bring all the food and water we have left, and all the scraps."
Magnus chuckled and pulled the hand from the chamber. "See, there's a mark where I wore my ring." He put the hand back. "If I take it out now, still another will appear."
"Did you have to use your hand?" Juan asked, feeling both relieved and repelled by the sight. "You might have lost it, for all you knew."
Lena nudged him. "Think what it means!"
"You have to take chances sometimes," Magnus said, "if you want to learn anything."
"Let's try it," Lena said. "I'm hungry."
Malachi gave them a sad look. "I should have saved one cigarette."
"Be happy you've quit," Lena said.