Have you ever heard of the Vagina Building? If you're not from Chicago, it's unlikely – but if you are, it's a precious part of local folklore and a celebrated shape on the skyline. Towering amid the clustered phallic skyscrapers, the Crain Communications Building (its slightly more official name) was completed in 1983 with a prominent vertical slit in the front. Urban legend – for sadly, that is all it is – states that the building was designed by a woman sick to her back teeth of phallic architecture as a big feminist middle finger to the men who had made her live in the shadow of their huge metal penis replacements for decades.

The truth is that the vaginal resemblance is accidental, and the architect behind it very much male. But the story persists, and is still told with a sense of pride. Luckily for all of us who enjoy a good story involving construction and genitalia, this week has proven that Chicago's Vagina Building will soon be rubbing, er, shoulders with another case of "accidental vagina representation". The design for Qatar's new Al-Wakrah sports stadium has quickly gone viral: with its shiny, pinkish tinge, its labia-like side appendages and its large opening in the middle, the supposedly innocent building ("based upon the design of a traditional Qatari dhow boat") was just asking for trouble. And trouble came, in the form of Buzzfeed and thousands of Twitter fans. Surely a well-populated Facebook group is only hours away.

As those who have tried to keep alive the tale of the Chicago Vagina Building know, there is something quite pleasing about a building shaped like a fanny. Look out on to the London skyline and penises are everywhere: the Gherkin, for instance, might even be visible from your office window right now, thrusting itself into the grey autumn sky among wisps of cloud, a proud red light shining at its very tip. And that's without even going into the phallic implications of Big Ben. The world even has an ode to the wonky boner, that lopsided erection that is the Leaning Tower of Pisa. Penile structures were just as abundant in the ancient world, of course – and while the humble yoni once had its heyday in certain parts of Asia, it still usually took a backseat wherever ornamental penises were involved.

The Qatari stadium's resemblance to a woman's private parts may be unintentional, but I for one applaud it. Perhaps the bigwigs who will be running the stadium should embrace this so-called faux pas and rebrand it as a deliberate nod towards the increasingly liberal Qatari policies concerning women in sport. In a world where sport and vaginas very rarely come together with such prominence (see every UK female footballer's salary versus every UK male footballer's salary), this can only be a good thing. And after all, why not have 45,000 people crammed inside a woman's reproductive system? It's not like they haven't been there before.

• This article was amended on 19 November 2013. It originally referred to "the bigwigs behind the design" probably being men. The architect was female, Zaha Hadid. This sentence has now been changed accordingly.