This scenario is based on three specific megastructures that are considered but never realized: Japan's Shimizu Mega-City Pyramid, 2004 meters tall and covering an area of eight square kilometers, planned to house one million people; Japan's X-Seed 4000, four kilometers tall and six kilometers wide and supposed to house 500,000 to one million people; and San Francisco's Ultima Tower, 1,828.8 meters tall, 140 square kilometers in area and having a capacity of one million people.
For this question, materials are not the focus here, as in an alternate history where the Industrial Revolution began in medieval China, they might have found time and materials to get around that problem. The real focus here is capacity because the postwar cities in this alternate Earth consist of only three different dimensions:
- Pyramids 2004 meters tall and covering an area of eight square miles
- Cylinders four miles tall and six miles wide
- Cubes two miles tall and covering an area of 140 square miles
By 1950, there were 12.5 billion people, 90% of which lived urban. Eurasia, Africa, South America and Australia's populations could be found primarily in either of those three shapes listed above. (North America, meanwhile, is stuck in its steampunk past because it'd be more expensive to demolish and rebuild a building than building a new one from scratch.)
Now the question is--what would be the maximum capacity of humans in each of the three shapes listed above?