The Tripura is one of the mind-boggling architectural structures mentioned in the Puranas such as Shiva Purana, Vishnu Purana, and Skanda Purana. The Tripura was not a single structure but three independent structures made of iron (or bronze?), silver and gold. The Puranas describe them as splendid cities floating in the sky. The architect, Mayasura has been praised for the grandeur of these cities and has been described as the major achievement of the Asuras (humankind?). The destruction of the city, too has been detailed. Lord Shiva using grand chariot, bow and a nuclear-like weapon called the Pashupatastra brings an end to the magnificient cities as well as the Asuras.
My aim here, though is not to feed the readers with the Puranic stories. I have been thinking about the story for some days regularly now (I have my own reasons for contemplation) and suddenly I came to think over the process by which the Tripura was built. It is not only about defying the gravity. There are many other things that seem unachievable that the Asuras achieved by constructing the Tripura. Yet the more I think of it, the crazier it gets. How could the Tripura have been made?
I have presented my questions point-wise and will try to explain them as simply as I can. They are in the chronological order as they appear during the construction and inhabitation of the Tripura. I have not presented any question on the destruction of the three cities. That may make up another article.
Question 1. Who did the penance to please Lord Brahma?
Every version story of the Tripura begins with a penance by three Asuras. But there is no unanimity upon who the penants were. One version tells that they were the sons of Tarak- Tarakaksh, Kamalaksh and Vidyunmali- after Tarak died in the battle from the hands of Kartikeya. The other version presents Tarak himself as the penant along with Maya (mentioned as Mayasura above) and Vidyunmali. Which of the trios pleased Brahma? This question is important to check whether the story we have known is a history or a myth. Had there been a single group of three penants, the story would be consistent. The two groups adds inconsistency and also loses the story's stance as a history. It becomes more inclined towards myth. 
Question 2. Where were the cities made?
This is the most difficult question I have come through. There are three possibilities. Within each possibilities, there are also problems which seem to have been overlooked (or I may not have understood).
The first possibility is that the Tripura was made on land. But the Tripura was a floating city- almost like the modern-day International Space Station. (Even grander!) How were three cities established to orbit around the earth. Yeah, their timing must have been different because they were on three different levels. But to establish a city on space, the Asuras must have launched a rocket and with precise calculations set them. Because Maya, Brahma and Shukra were on their side during construction, we can assume that they achieved the feat, but the Earth had been scoured by the Deva-Asura war. There was no chance the Devas would let the Asuras make such huge structures with ease. With the Earth under their rule, Asuras have been said to have resorted to the Patal, the Underworld. Construction of three grand structures on land seems difficult.
So, we move to the second possibility- the sky. If you are making something that floats on space, why not make it on space? But let's observe the modern trend. Do we make satellites on the space or on the land? Obviously, building satellites on sky would be difficult because of the huge number of materials needed to be transported up above the escape velocity. A huge consumption of fuel and time. Also, building anything on space would require huge amount of oxygen supply, and good insulation of workers against the solar flares. Could the A sure have obtained it? Building castle on space is even more difficult that building it on air. And they made three. The possibility of the Tripura being built on sky seems thinner than the atmosphere there.
The third possibility is that the cities were made in Patal. They were shot up in the sky and were fixed on their orbit.The problems mentioned on the first two possibilities are still prevalent.
To have built such grand structures without the intervention of the Devas would be an almost impossible feat. The Asuras did it brilliantly. And that is the biggest wonder ever.
Question 3. How did the residents of the Tripura reach there?
The Puranas not only describe the construction but also the settlement. A huge numbers of humans including Asuras, Manusyas, Apsaras, Gandharvas, Yakshas, Nagas are said to have lived there. How Maya and his contemporaries provided their need of oxygen and food is the question that actually troubled me. Without the mention of some device that helped them breathe and control gravity, the settlement would be too difficult. How did such a huge number of people migrate to the Tripura? Did they have spacecraft? Of what sizes? Also, the three penants ruled upon the cities. What did they use to travel between the cities? Transportation would be simpler with Vimanas (aircrafts/spacecrafts) but the number of people who lived there must have required a huge number of them. Who would have mass produced them? Maya and his team of scientists? That's a faint light of hope if I would be taken to the mythological Tripura. Everything else looks an almost impossible feat to me.
[N.B.: 1. The Asuras do not necessarily mean evil neither do Devas always mean good. In fact, Indra, Agni, Vayu (Devas) have been called Asuras in the Rig Veda.
2. I disagree with the popular belief that Vyas was the writer of all the Puranas. One person would not have made the mistake of writing different names of the Trios that pleased Brahma. Either the stories were modified with time or the Sage made a mistake unknowingly.
3. The Tripura was not just an architectural marvel but it was also (and is till date) an advanced technological achievement (considering Puranas speak history). Else it was the best thing that could be imagined by the writer (Vyas?) of the story.
4. No city can flourish without human settlement and their activities. A lot of resources are needed to sustain lives. How they were provided would provided in a satellite city could be a topic of debate.
5. This article is in fact an arrow in the darkness. I may not get an answer here. Yet, it is a beginning and I expect someone to go through this article and begin questioning on the things that they might have overlooked in the story. I also expect(with rare probability) the logical and more scientific answers to these questions. That means, divinity will be out of the equation. "Divine interference/involvement" is an answer that kills our reasoning abilities.]
iv. Shree Swasthani Vrat Katha (A part of Magh Mahatmya of Skanda Purana)