A manufacturing future that hums (rattles, hisses) along

FORTUNE — Every day, the young, bearded, and tattooed team at the Shapeways factory in Long Island City, Queens gather to eat together, as if they lived in a 19th century company town. There aren’t many dining options in the industrial area in which they work, so they order takeout pizza or food from FreshDirect and convene. Their routine is fitting: Shapeways, a three-dimensional printing company, tips its hat to the industrial past even as it seeks to reinvent manufacturing.

On almost every flat surface in Shapeways’ open plan office are whimsical creations — multicolored figurines of humanoid creatures, skeletons of imaginary animals, abstract sculptures that appear inspired by nature’s curving forms. There is even a fractal design of a deer’s head that looks like the frame on which you’d hang the real thing.

All of this illustrates the powerful potential that 3-D printing has to create an infinity of objects. The technology that makes 3-D printing possible has existed for decades, often employed as a prototyping tool in sophisticated industries such as aerospace. More recently, the do-it-yourself community and other hobbyists in the so-called Maker movement have adopted it as a way to create novel items. Now that the technology is no longer in doubt, Shapeways is betting that 3-D printed objects have a place in every home.

Shapeways was founded in the Netherlands in 2007 and incubated by the electronics giant Philips. It hosts an Etsy-like online marketplace of more than 13,500 online storefronts where designers showcase countless products, from figurines and credit card holders to jewelry and kitchenware. Last year, it raised $30 million in venture capital from heavyweight firms including Andreessen Horowitz. It’s now headquartered in Manhattan, across the river from the factory.

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The Shapeways marketplace works like this: Customers search for items at the Shapeways site. After finding a design of interest and selecting a preferred material, the request is sent to staffers at the Shapeways factory, who determine if it is feasible. Then the printers whirr into action. Shapeways didn’t develop its 3-D printing technology, but it turns it into a consumer-facing business by manufacturing creations, reviewing them for defects, and dyeing or polishing them into finished products before shipping them.

The term “3-D printing” doesn’t refer to a specific process so much as a category of processes that are each capable of creating one-of-a-kind items. Desktop 3-D printers often rely on an “extruding” process in which a material is fired into a shape and then solidified. It’s sort of like a glue gun shooting both the glue and whatever it’s holding together.

Here at the Shapeways factory, the company uses a process called laser sintering in which each item gets fused together layer by layer. The material starts in a powdered form, and when a laser scans across it, it hardens into a layer that will, in aggregate, comprise the final product.

Mainstream manufacturing processes like injection molding are very good at producing an infinite number of identical products, but there are physical limitations to what can be created. 3-D printing changes the manufacturing process in at least two interesting ways: It allows for the creation of incredibly intricate designs (such as a pre-assembled chain of links) and makes it easier and less expensive to create one-off or limited-run creations. The design software acts as a conduit between the designer’s brain and the printer, limited only by her imagination and the laws of physics.

For example, an artificial tree printed in 3-D would begin at the bottom and add parts of the trunk, branches, and leaves with each successive layer — regardless of the complexity of each horizontal. Since the structure of a tree is so complex, an artificial tree produced with standard manufacturing technology might involve the creation of separate molds for the trunk, branches, and each individual leaf, and then require assembly.

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With 3-D printing there’s “no cost of complexity,” Carine Carmy, Shapeways’ marketing director says.

The printers at Shapeways’ factory are produced by a company called EOS. The machines are the size of large refrigerators with a window on the front to peer inside. When the author glanced in during a tour of the space, he saw several items under construction — though it was difficult to make out just what they might be.

Beyond the printers is a rock tumbler the size of a round dinner table, used to smooth out the rough edges of a newly printed item. When it is turned on, the machine is so loud that you can’t stand to be in the room with it.

At the end of the line, there are bins for sorting. Like the rest of the factory it seemed relatively quiet during a recent visit, suggesting that mid-winter isn’t the high season for individualized products.

Shapeways chief executive Peter Weijmarshausen says the Shapeways marketplace, which launched in 2009, is like Apple’s App Store in that both facilitate creative entrepreneurship. Weijmarshausen says his company sold 1.2 million pieces last year, and he expects volume to triple this year. (He declined to comment on revenue.)

Despite the hype around 3-D printing, you need only look around the American home or office to see that this industrial process has not yet insinuated itself in daily life. But it’s already in use by major U.S. manufacturers: General Motors and Ford, for example, both use the technology to speed up the design and prototyping process.

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The prospect of individualized manufacturing has lots of people excited. Some of the more feverish prognosticators say it could upend the global supply chain and reshuffle the geopolitics. It could revolutionize medical devices, and much else.

And so the technology has attracted business interest. Last year Stratsys acquired MakerBot, which manufactures a relatively affordable desktop 3-D printer, in a deal that could ultimately be worth more than $600 million. While MakerBots could theoretically become household items, Shapeways is instead charting a path of decentralized creativity but centralized manufacturing. Shapeways must now figure out how to sell unique and beautiful items to consumers who don’t fetishize the process of 3-D printing.

Weijmarshausen says that the technology has already cleared several barriers to adoption. 3-D printers were once “horrendously expensive” and required highly specialized software; they are more accessible now. The next step is relevance, he says, which “comes from great stories that people care about.” (Because while a 20-sided die may be inventive, it’s still as practical as, well, a 20-sided die.)

As it grows, Shapeways has to conquer what Carmy calls the “blank page” problem: Just because customers say they want unique things most doesn’t mean they will devote much time or effort to acquire them. And products that encourage personalization, like last year’s Moto X smartphone, don’t always succeed even when the options are far more limited.

To address this, Shapeways has introduced several web apps to facilitate creativity. With one program, users can turn a drawing into a 3-D bauble. Shapeways has also released apps to let users customize a ring or sake set, as well as a toolbox for more sophisticated designers. Shapeways also announced a partnership with Adobe that lets users upload and manufacture Photoshop creations.

“Everyone is more creative than what we call ‘big brands’ today,” Weijmarshausen says. “No more lowest common denominator.”

It’s a fine goal, but difficult to achieve in practice. Kostika Spaho, a designer who has sold products on Shapeways for several years, has designed a line of otherworldly coffee cups and co-designed a “biomimicry shoe” inspired by the shape of a bird’s skull. But his best-selling products on Shapeways are based on Internet memes. His No. 1 product, he says, is this obstreporous anteater, “Due to the fact that it’s already popular and a lot of people know of it.”

“Instead of thinking of what products I should make, I go to Reddit and ask people what they want,” he says. This has led to such innovations as a desktop catapult that clamps to the corner of the desk. “It’s so ridiculous, but this is what they want.”

Spaho pauses. “I would like to make sexy, beautiful products like the cups and the shoes,” he says. “But they don’t sell.”

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