One World Trade Center, more simply known as 1 WTC and previously known as the Freedom Tower, is the lead building of the new World Trade Center complex in Lower Manhattan, New York City. The supertall skyscraper is 104 storey  and is being constructed in the northwest corner of the 16-acre World Trade Center site. The image at the right shows the design as of May 2012.

One World Trade Center is an example of an antiprism. The square edges of the world trade centre tower’s cubic base are chamfered back, transforming the building’s shape into an elongated square antiprism with eight tall isosceles triangles—four in upright position and another 4 in upside down direction. Near its middle, the tower forms a perfect octagon, and then culminates in a glass parapet whose shape is a square oriented 45 degrees from the base. My question is Is this bigger than if it were a square prism? How about in terms of surface area?

Antiprisms are similar to prisms except the bases are twisted relative to each other, and that the side faces are triangles, rather than quadrilaterals. Here’s a model of a square antiprism.

square antiprism

The surface area of the antiprism may be bigger than the prism because of the additional faces but I’m not quite sure. How about the volumes? Cavalieri’s principle does not apply because the cross sections do not have the same area. Anyone wants to resolve and explain this? There is a formula for volumes and surface areas of antiprisms but I’d appreciate a more intuitive solution.

Note: All information and images about 1 WTC is from Wikipedia. Square antiprism model from eusebeia.dyndns.org.

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