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Roger's Connection®
O
N-LINE INSTRUCTION MANUAL

# Building the Tetrahedron

## Starting with a Triangle

A tetrahedron has 4 sides, 6 edges, and 4 vertices. With Roger's Connection, that translates to 6 magnetic tubes, and 4 connector balls. There are many ways to build this polyhedron, and three different approaches are shown here. Each of the three ways will give you a different sense of the tetrahedron, and highlight different aspects of it. Here is the first approach, in which the tetrahedron is build up from a triangle.

 Step 1 2 3 4 First, using three balls and three tubes, construct a triangle, shown here in blue. Next, attach three tubes to a single ball, forming a tripod shown here in red. Finally, connect the three free ends of the red tripod to the three balls of the blue triangle. Congratulations! You have just constructed a tetrahedron, the simplest and most basic of all the polyhedra.

# Building the Tetrahedron

## Starting with a Ditriangle

Here is a completely different approach to building a tetrahedron, based on using a Ditriangle. A Ditrangle is simply two triangles, back-to-back. You can also consider the ditriangle as having started as a square, black in the first picture below, which has been cross-braced with the blue tube.

 Step 1 2 3 4 First, using four balls and five tubes, construct the ditriangle shown here. Next, fold up one of the triangles along the blue tube. Finally, add the last tube shown here in red to complete the tetrahedron. And here once again, is the completed tetrahedron.

# Building the Tetrahedron

## Starting with a Square

And here is yet another approach to building a tetrahedron, based on using a square.

 Step 1 2 3 4 First, using four balls and four tubes, build a square as shown here. The black, red, and blue color codes will help keep things straight in the following steps. Next, place one of the black sides of the square on your work surface, and hold the other black side in the air, directly above the black tube below. Keep the blue tube to your left, and the red tube to your right. Next, keeping the black tube on your work surface from moving, rotate the black tube above it a quarter of a turn counter-clockwise. Looking down from the top, this is what it should look like. Finally, add two more tubes, shown here in yellow between the top and bottom balls that are not yet connected. Congratulations! You have once again built a tetrahedron. Notice that when you added the last two yellow tubes, you cross-braced the original square in two different ways, converting the unstable square, into a very stable tetrahedron, formed entirely of triangles. Here is the final tetrahedron. The view might look unfamiliar, but it IS the same tetrahedron as before, just rotated into a different orientation. This view of the tetrahedron, which shows the central tubes crossing at right-angles, shows how the angles of a square or a cube (90 degree angles) can be found hiding inside a structure made entirely of triangles.

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