Can you say, “POOHG”?
( “H” is silent )
2001: Learn about the interiority of the octahedron: The students learn about the most-simple, perfect configuration within an octahedron. There are fourteen pieces, six smaller octahedra and eight tetrahedra. All fourteen pieces share a common center point.
Notice in our image of that octahedron, some of fourteen pieces have edges that have color. In this image, we’ve used red, white, blue and dark green. Notice each color creates a hexagonal plate. The white and red plates are most readily identified in the image on the right. The blue and dark green plates are a bit obscured. The taping of pieces is still a bit crude at this point in time. This is the first generation of the game.
The object of the game is to reconstruct the four plates as given when the pieces are all emptied onto the table. Sounds simple. It’s not!
The competition can be between as few as two and as many five. Four seems ideal. Reconstructing the octahedron with the four plates as seen for some will be intuitive. After doing it a few times, we’ve had people put it back together in just under a minute while others have tried and tried but not succeeded.
Use a three-minute timer with a verbal 15-second warning (just to keep the game moving) so with four students, each set of the competition takes a little more than 12 minutes. Winners then compete, and eventually we have a winner for the class, then a winner for the grade, and then a winner for that semester.
With extra sets on hand for those who get timed out, everybody eventually wins because now they have seen and felt the interiority of the octahedron and can readily apply it in other studies within the curriculum.
There are other games we’re developing with the octahedron and tetrahedron that are very similar but not quite as much fun. We’re working on it!
Every new game will be posted right here.
Editor’s note: On 4 March 2025 a new challenge is added. We are speculating in a most-confident manner that these four plates are the faces of the four primary irrational numbers that go off within infinity forever.
There has got to be a game or two intertwined with this hypostatization! -BEC
History: We had the clear plastic models fabricated in 1999 in San Diego where we were living at the time. Clear tetrahedrons and octahedrons were made by the hundreds. The first images were of the tetrahedron with its four internal tetrahedrons and its octahedron. We first used it on one of our television shows to demonstrate the intimacy of +Products-People-Processes in business. This image comes from https://smallbusinesschool.com
Many years later (2022), I was still thinking about these basic structures when I pondered, “Could five octahedrons share a common edge? Would there be the gap?” Of course, we found the same gap. There was no articles on line about it. Before we could truly believe it, we had to see a model of it.
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