Not just any old building, mind you, but one with a gleaming metallic facade and sharp angles, the first residential property in Europe by architect Daniel Libeskind.
"We haven't set a price yet," says silver-haired softly spoken developer Nikolaus Ziegert.
Sapphire is still a construction site - but on a whistle-stop tour, it's easy to see its appeal to foreign wealthy buyers.
In many ways, this $43m (Â£29m) development symbolises the gentrification of the city.
It's certainly set tongues wagging, dividing opinion in the historical district of Mitte.
The luxury property market is red hot in this neighbourhood.
Almost everywhere you look from the roof of Sapphire, there are cranes at work, constructing a new Berlin.
Just over a decade ago, Berlin's mayor declared the city "poor but sexy", a reputation that helped attract innovative and creative businesses.
But now, with its fortunes rapidly changing and the gentrification this brings, is Berlin in danger of becoming a victim of its own success?
Its population has been growing fast, and in the past five years so have rents, pricing some local residents out.
For Mr Ziegert, business is booming.
He set up his property company 30 years ago in West Berlin, when the city was still divided, with just three employees.
Now, he has a turnover of some $300m, and 180 staff.
Mr Ziegert enjoys being chauffer driven in a vintage Maserati. But he doesn't fit the stereotype of a brash property developer.  He is aware of the tensions development can create.
"Gentrification has to be seen from two angles," he says.
"Of course, the first is that of the tenant.
"In Berlin, when the prices rise, people feel insecure.
"On the other hand, gentrification also means change and progress.
"And even if it's unpleasant for some, it remains very important for the city that investment comes in."
In many ways, Berlin is still a city of two halves.
On the one hand, there is an incredibly fast-growing community of hi-tech start-ups.
On the other, the city's unemployment rate is more than 10%, compared with just 6% for the rest of Germany.
Michael Plaumann lives in a homeless shelter in Neukoelln, an area earmarked by developers as the next property hotspot.
To supplement his unemployment benefit, he sells a homeless newspaper on the trains of Berlin.
"It's very difficult for me to find my own apartment for myself," he says.
"That's why I've been living in a shelter for a while already, because the apartments have become very expensive, and for as someone who receives benefits, it is just too expensive."
The $900 (Â£600) cost of his shelter accommodation is covered by his benefits.
Should he find an apartment of this own, he'd be unable to claim the full rent because of a cap, which could price him out of his neighbourhood.
"I want to live in my neighbourhood. That's Neukoelln. I've been there for 15 years," he says.
"What bothers me is that in Berlin, more and more neighbourhoods are becoming ghettos. Berlin is not changing for the better."
Lisa Jaspers earns not much more than Mr Plaumann gets in benefits and wages. But she's happy.
She set up her own company two years ago, after quitting her well paid job in the development sector.
Her business, Folkdays, is an online fair-trade fashion-and-accessories business, sourced from artisans around the world.
"We create designs that we knew that they can do," she says.
"And we actually sell our products online because it means we can actually offer our products for a price that is not crazy high."
Ms Jaspers also lives in Neukoelln, the same neighbourhood as Mr Plaumann, an area that typifies the gentrification of Berlin.
"I see pros and cons," she says.
"I have to say I'm pretty happy about the fact that so many people from all over the world want to live here."
The fall of the Berlin Wall brought freedom and inspired a cool and creative scene.
Low rents encouraged a lively alternative music and nightclub scene, in many ways the foundation of modern Berlin.
Roger Baptist, otherwise known as Rummelsnuff, worked as a bouncer for many years before he made music his full-time career.
He has over three million hits on YouTube, a record deal and a film in the pipeline. The 49-year-old lives on a former World War Two barracks.
"It's not Beverly Hills," he says as he gives me a tour.
He has an improvised recording studio, and the music he produces earns him just enough money to do what he wants.
"The danger for Berlin, especially inner-city Berlin, is that people move there and because it's a clubbing neighbourhood [they complain] it's too loud, they make reports to the police and the clubs have to close," he says.
"We need a loud inner city otherwise it gets boring."
Rummelsnuff is a mixture of Popeye meets electropunk - mainstream he is not.
Like many musicians, he was drawn to Berlin for its energy, open attitude and affordable rents.
Development is necessary to fuel Berlin's economic growth - but the more there is, the danger is the less attractive it will become for the artists and creatives.
This cultural vibe has helped attract an influx of well-paid professionals from the rest of Germany and beyond.
Bigger companies are moving in, too.
Berlin's research-and-development industry is growing so fast it's been dubbed Silicon Alley.
Julia Leihener works as an "ideation manager" for Deutsche Telekom.
She and her team develop new technology ideas, from smart-home technology to the future of mobile phones.
She arrived here 15 years ago and still thinks it's a great city to work in, but she has concerns about the commercialisation of Berlin.
"It's good and bad if money's coming in," she says.
"Where I live, I really see how it's been polished up and brought me to the point where I moved because it gets too polished.
"There's a great tension building up, and I can feel that in my area."
Berlin still has some way to go before it reaches the gentrified unaffordable capital many people predict it'll become.
The big challenge is how it continues to combine its creativity with capitalism, without losing what makes it so special.
Mr Ziegert believes his luxury development, Sapphire, represents the new Berlin.
"This is a great example of how [the] highest culture and highest art can at the same time be an interesting investment," he says.
"Simultaneously, Berlin is transforming and developing in a way that Berlin has waited for, for many, many years
"The challenge is to find the balance between the past and future, rich and poor, between art and functionality, and, for me, Daniel Libeskind is the architect that represents art in architecture and living art."
As for the penthouse?
"We're very excited about who is going to buy this in the end. We're not in a rush, we'd rather wait for a buyer to appreciate this unit."
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