Making Tesseracts

Supersize	SACAM brought local high school students into ORNL for three hours on eight Saturday mornings. They learned different ways computers and mathematics are used in a laboratory research environment. They used really great NeXt machines that were far ahead of other PCs of their time.
Supersize	The laboratory provided Top-Notch professionals like Dr. John Wooten (physicist) to mentor the students for their SACAM Saturdays. Dr. Wooten actually led the SACAM program for many years. Some of the students went to Washington DC as a result of the program. One young lady even served as a Washington Intern as a result of her involvement in the SACAM program.
Supersize	There are many different ways to create 4-space cubes more commonly known as Tesseracts. During this session students were shown how to create two different types of 3-dimensional Tesseracts. They're beginning to construct one here.
Supersize	The first type of Tesseract was created by cloning a single cube and displacing the clone from the original cube a little bit in each of our normal three dimensions. The displacement in this case was about eight inches in each of the X, Y, and Z dimensions. When you connect the same point (or corner or node) on each cube to its corresponding point on the other cube you get a 4-space cube or Tesseract.
Supersize	A second style of Tesseract is almost complete here. It is a cube within a cube where (again) each point of the larger cube is connected to its corresponding point on the smaller cube.
Supersize	The students have finished the displaced style of Tesseract and are admiring their handywork. This part was done completely without math.
Supersize	It is interesting to note that when viewed from different angles this Tesseract looks almost totally different. This is a picture of the same (displaced) Tesseract as before.
Supersize	It would be exceedingly difficult to hand-create an 11-space cube (an 11-cube). For that task you need binary operations and binary math. The math is really elegant in its simplicity. Here you see a two-dimensional representation of an eleven-dimensional cube.
Supersize	As I said before, there are all sorts of ways to draw N-cubes. One way is to place all the points of the N-cube in a circle and just make certain that each of the points is correctly connected to the other points. The 11-cube shown here doesn't look even remotely like a cube anymore, but it is topologically equivalent. One of the N-cubes here looks all twisted up, so it is called a Twisted Circle N-cube. It turns out you can untwist those points and that type is called an Untwisted Circle Cube.
Supersize	After creating two types of 3-dimensional, 4-space cubes, and creating 5-space cubes on the labs NeXt machines, the students were introduced to a research problem where they tried to discover specially defined maximal length closed loops (paths or snakes) through 3, 4, and 5-space cubes. The long green thing in this picture is a 4-space snake curling along the edges of a Tesseract. Students were able to discover 5-space snakes on their own and were introduced to a computer program designed to find 7-space snakes.