Antiprisms—Video Transcript In Lower Manhattan, a single tower With a square antiprism, there’s an plays a dual role. One World Trade interesting phenomena that happens Center, also known as the Freedom to the shape of the antiprism. When Tower, is both a skyscraper with many seen from above, we can sketch the floors of office space and also a outline of the antiprism. See the monument. It is a monument to the outline of an octagon? The triangular Twin Towers, whose imprint now sides create an octagon outline. makes up a memorial to that pivotal If we slice the antiprism with a plane, day in American history. each of those slices between the The Freedom Tower took many years square base and top are octagons, but to complete and went through several there’s only one octagon that is a iterations of its design before the regular octagon, and that happens at architects arrived at the final design. the midpoint of the height of the Geometrically, the One World Trade antiprism. Center is an antiprism with a square The same goes for the Freedom Tower. base. There is a continuous octagonal shape An antiprism has a polygon base with to the tower but only in the middle triangular sides. The base and top are floors is it a regular octagon. congruent but are at an angle to each One World Trade Center is a very tall other. Here is an antiprism with a antiprism, but it still has the properties triangular base. Here is an antiprism of a square based antiprism. There are with a square base. six huge isosceles triangles along the The number of sides of the polygon sides of the tower. base determines the number of This is a simplified scale model of the triangles on the side. A triangular Freedom tower. There is a rectangular antiprism has six triangles, as you can base from which the antiprism shoots see from this animated sequence. A up into the sky. On each floor of the rectangular antiprism has eight tower the floor plan is an octagon. triangles, as shown here. In general, an n-sided polygon results in 2n triangles There is also a metal spire at the top of on the side. the tower, giving the full structure a 1 total height of 1776 feet. The America. significance of this number is that it refers to the year 1776, when the Declaration of Independence was written and signed—the time that America declared itself a nation free of the British monarchy. This is one reason One World Trade Center is referred to the Freedom Tower. However, the fact that it is also called One World Trade Center is a reference to the North Tower of the original World Trade Center. This idea of the dual nature of the Freedom Tower is also reflected in its geometry. As you saw earlier, an antiprism can be split into two congruent figures, each with a square base and four triangular sides, as shown here. An interesting feature of a half anti- prisms is that it corresponds to a net for a square pyramid. In fact, the half- antiprism is midway toward the pyramid, and this animation completes the construction. So, the Freedom Tower’s geometry holds the key to two tall pyramids, and since pyramids are often monuments to the past, the same holds true here. The two virtual pyramids in the Freedom Tower are an allusion to the twin towers, the predecessors to this new magnificent tower. In this way, One World Trade Center serves as a monument to this important part of 2 .