Roger's Connection


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Roger's Connection^®
ON-LINE INSTRUCTION MANUAL

Building the Octahedron

Starting with a Square

An octahedron has 8 sides, 12 edges, and 6 vertices. With Roger's Connection, that translates to 12 magnetic tubes, and 6 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 octahedron, and an insight into how it is related to other polyhedra. Here is the first approach, in which the octahedron is build up from a square.

Step 1 2 3 4

First, using four balls and four tubes, construct a square, shown here in black. Next, attach four tubes to a single ball, forming a "quadpod" (like a tripod, but with four legs instead of three). The quadpod is shown here in blue. Next, attach the blue quadpod to the black square. Congratulations! You have just created a pyramid! Now carefully turn the pyramid upside down, so that the original black square is now facing up. Next, prepare another quadpod with one ball and four tubes, shown here in red. Finally, attach the red quadpod to the black square as shown. Congratulations! You have just successfully completed the octahedron!

Building the Octahedron

Starting with a Two-Frequency Triangle

Here is a completely different approach to building an octahedron, based on using a two-frequency triangle.

Step 1 2 3

First, using six balls and nine tubes, construct a two frequency triangle, shown here in black, with an inner triangle of blue. Next, fold up the three outer triangles along the blue tubes as shown here. Finally, add three additional tubes, shown here in red, to connect the three balls at the top.

Building the Octahedron

Starting with a Trigonal Prism

And here is yet another approach to building an octahedron, based on using a trigonal prism.

Step 1 2 3

First, using three tubes and three balls, build a triangle, shown here in yellow. Next, attach three vertical tubes, shown here in red, to the three balls of the yellow triangle. Finally, add another triangle to the top, shown here in blue. Congratulations! You have just constructed a trigonal pyramid! Next, with theyellow triangle resting on your work surface, rotate the blue triangle on the top 1/6 of a turn in a clockwise direction. This picture is a top view of what you should now have. Finally, connect the final three tubes, shown here in black. This is also a view looking down from the top. Each of the three final black tubes should connect from one of the three balls of the blue triangle on the top, to the ball of the yellow triangle on the bottom that is 1/6 of a turn clockwise from it. Congratulations! You have again built an octahedron. Notice that when you added the last three black tubes, you cross-braced each of the three unstable squares on the side of the original trigonal prism. This turned each of these unstable squares into two stable triangles, finally resulting in a stable octahedron.

Step 1	2	3	4

First, using four balls and four tubes, construct a square, shown here in black. Next, attach four tubes to a single ball, forming a "quadpod" (like a tripod, but with four legs instead of three). The quadpod is shown here in blue.	Next, attach the blue quadpod to the black square. Congratulations! You have just created a pyramid!	Now carefully turn the pyramid upside down, so that the original black square is now facing up. Next, prepare another quadpod with one ball and four tubes, shown here in red.	Finally, attach the red quadpod to the black square as shown. Congratulations! You have just successfully completed the octahedron!

Step 1	2	3

First, using six balls and nine tubes, construct a two frequency triangle, shown here in black, with an inner triangle of blue.	Next, fold up the three outer triangles along the blue tubes as shown here.	Finally, add three additional tubes, shown here in red, to connect the three balls at the top.

Step 1	2	3

First, using three tubes and three balls, build a triangle, shown here in yellow. Next, attach three vertical tubes, shown here in red, to the three balls of the yellow triangle. Finally, add another triangle to the top, shown here in blue. Congratulations! You have just constructed a trigonal pyramid!	Next, with theyellow triangle resting on your work surface, rotate the blue triangle on the top 1/6 of a turn in a clockwise direction. This picture is a top view of what you should now have.	Finally, connect the final three tubes, shown here in black. This is also a view looking down from the top. Each of the three final black tubes should connect from one of the three balls of the blue triangle on the top, to the ball of the yellow triangle on the bottom that is 1/6 of a turn clockwise from it. Congratulations! You have again built an octahedron. Notice that when you added the last three black tubes, you cross-braced each of the three unstable squares on the side of the original trigonal prism. This turned each of these unstable squares into two stable triangles, finally resulting in a stable octahedron.