Google Earth Voyager Story: Architectural Prisms, Part 3

Not all prisms have rectangular sides. In particular, antiprisms have triangular sides. One noteworthy example of this in New York is One World Trade Center, also known as the Freedom Tower. Its geometry is that of an antiprism with a square base. In this lesson we will be exploring antiprisms, especially in the context of the Freedom Tower. This is part of a lesson on Google Earth. To see the Google Earth version of this lesson go to this link (best viewed in Chrome).

Note: We also have related lessons on these topics:

1. Introduction: Prisms

Before diving into antiprisms, get a broad understanding of prisms. Watch the following video, which includes a discussion of antiprisms.

 

2. Applications of Rectangular Prisms: The Freedom Tower

Now that you have a basic understanding of prisms and antiprisms, let's take a look at an example of a building based on an antiprism design, One World Trade Center. Watch the video to learn more.

3. Constructing an Antiprism

An antiprism with a square base has two square faces and eight triangular ones. Watch the animation to see what an antiprism is supposed to look like.

 

To construct an antiprism use a net like the one shown here. Print and cutout the net, or construct one of your own. (Click here for a printable version of the net.) The video shows how the net folds into an antiprism. Note: The net shown below includes flaps to use glue in constructing the prism.

 

Follow these steps to create your triangular pyramid using the net:

  1. Print the net.
  2. Cut the net along the outline. Be sure to include the flaps.
  3. Fold along all the lines, including the flaps.
  4. Working on one side at a time, place glue on the flaps and attach them to the underside of the opposite side.
  5. Repeat with the other side of the net.
  6. Let the glue dry before handling the net.

4. A Scale Model of the Freedom Tower

Now that you know how to construct an antiprism, use your knowledge to build a scale model of the antiprism portion of the Freedom Tower. Use the following information about the tower:

  • Use a base-to-height ratio of 6:1.
  • Try to get your net to look like this in shape.
  • Be sure to include flaps to make it easier to glue the sides together.