At 58 storeys high, Trump Tower is not the largest skyscraper to grace the streets of New York, but it is big. Imposing. Dark. It sits not far from the southernmost edge of Central Park, and it is a surprise, when you find it, to discover that it really does exist. It seems like a comical invention, a ludicrous temple to a bizarre god. And yet here it is, huge and mirrored and very, very real.

The construction of this beast was anything but smooth, marred as it was by controversies surrounding the underpayment of contractors and the blithe destruction of valuable architectural works of art. Once complete, however, it was very soon occupied. Much of the tower is taken up with residential and office space, but there are a number of floors that are open to the public. Visitors are, for want of a better word, welcomed most days of the year.

1. Security

There are men with guns at the entrance, squinting imperturbable through sunglasses. Concrete barriers bisect the streets on each side. The first word you think of when you look up at its mirrored planes is “fortress”. And yet inside it is as pleasant and welcoming as any other shopping mall. You almost have to double check that you’ve come to the right place.

2. The Lobby

The greeter is earnest and friendly. Which surprises you. You’ve keyed yourself up to believe that you are on enemy territory. That they are looking at you with distrust. But he apologises profusely that the terrace is unavailable, and tells you with genuine sadness in his voice about the fire that made it so a few months before. In manner he reminds you of the man who showed you how to fire a gun at the shooting range in the middle of the desert: gentle, friendly and quiet – keen to show you that he is not dangerous. That these is nothing dangerous here.

3. The Gift Shop

You can buy everything here. Trump cologne comes in two varieties, “Empire” and “Success”. The novel that was originally published under his own name is now republished under the name of the ghostwriter, endorsed as, “The sexiest novel of the decade”. There are chocolate snacks shaped like gold and silver bars (both cost the same), babygros, popcorn, souvenir pens, whole vats of Trump-branded keyrings.

4. Melania’s Store

It is almost unbelievably small – a narrow pinkish enclave stocked with less than fifteen handbags, a bored-looking clerk lingering by the till tucked against one wall. The wares are expensive but bland, and although the little cubby is adjacent to the thronging public atrium, nobody stops to look at them.

5. The Trump Bar

Drink here and you’ll find yourself on a balcony level, looking across the void at your own warped, indistinct reflection in the distant copper-panelled wall. You are inside a church dedicated to wealth, and it is not an entirely unpleasant place to be. The waiters are deferential to the point of pain. They do now know you, but there are plenty of offers of something to drink.

6. Up

You can only go so far. Three levels of ascending escalators, each one bridging an increasing void. Below you, people mill. It is quiet up here. As promised the terrace is closed until further notice. Signs warn that you must wear the correct shoes. You linger here a moment. Above you an unimaginable wealth of office space and luxury housing. A world that you are not party to, that you are an irrelevance in. You wonder what you would think if you lived in such a place.