Antiprisms.mp4

Antiprisms--Video Captions

In Lower Manhattan, a single tower plays a dual role.

One World Trade Center, also known as the Freedom Tower, is both a skyscraper with many floors of office space and also a monument.

It is a monument to the Twin Towers, whose imprint now makes up a memorial to that pivotal day in American history.

The Freedom Tower took many years to complete and went through several iterations of its design before the architects arrived at the final design.

Geometrically, the One World Trade Center is an antiprism with a square base.

An antiprism has a polygon base with triangular sides.

The base and top are congruent but are at an angle to each other.

Here is an antiprism with a triangular base.

Here is an antiprism with a square base.

The number of sides of the polygon base determines the number of triangles on the side.

A triangular antiprism has six triangles, as you can see from this animated sequence.

A rectangular antiprism has eight triangles, as shown here.

In general, an n-sided polygon results in 2n triangles on the side.

With a square antiprism, there's an interesting phenomena that happens to the shape of the antiprism.

When seen from above, we can sketch the outline of the antiprism.

See the outline of an octagon? The triangular sides create an octagon outline.

If we slice the antiprism with a plane, each of those slices between the square base and top are octagons,

but there's only one octagon that is a regular octagon, and that happens at the midpoint of the height of the antiprism.

The same goes for the Freedom Tower.

There is a continuous octagonal shape to the tower but only in the middle floors is it a regular octagon.

One World Trade Center is a very tall antiprism, but it still has the properties of a square based antiprism.

There are six huge isosceles triangles along the sides of the tower.

This is a simplified scale model of the Freedom tower.

There is a rectangular base from which the antiprism shoots up into the sky.

On each floor of the tower the floor plan is an octagon.

There is also a metal spire at the top of the tower, giving the full structure a total height of 1776 feet.

The 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 as 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-prism 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 small 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 America.