I have a lot of information about the Jitterbug dynamics to share with you. It is easier to visualize the information with a 3D interactive program.
So, here is an interactive web page that lets you explore Jitterbug and some of the associated polyhedra. Below I will show you how to use some of the program's features as well as describe some of the Jitterbug's relations to polyhedra.
The controls to the interactive web page assumes a 3-button mouse.
The left button will rotate the scene displayed.
The center button or wheel will zoom the scene in and out.
The right mouse button will drag the scene with the mouse.
I am not familar with Apple computer, so I do not know what the equivalent mouse functions will be.
I will now walk you through using the Jitterbug interactive web page.
When you go to the web page, it is blank with a column of buttons on the left. These buttons turn the display of various Jitterbugs and other objects in the scene "on" and "off". All objects start with their display mode "off". Clicking on one of the buttons will toggle the object on or off if it is currently being displayed.
Click on the "JB #1" button. It will display a Jitterbug in the Octahedron position.
Click on the "Animation" button to start the Jitterbug dynamics. Use the mouse controls to change the point of view and size.
Click on the "Axis Line" button to display the 4 axes that the Jitterbug triangular faces are rotating about.
During the Jitterbug motion the Jitterbug passes through special positions which correspond to various other polyhedra. These special positions can be displayed by clicking on the "Poly. Positions" button. It is easier to see if you also click on the "Ellipse #1" button to display the ellipse around which some of the Jitterbug's vertices travel.
We can also remove the Jitterbug to see all of the special positions.
The color coding of these special positions is as follows:
Gold = Octahedron,
Blue = Dodecahedron, Cube, and Tetrahedron,
Green = Icosahedron,
Red = Cuboctahedron (VE).
Here the Jitterbug is ine one of the Icosahedron positions. We have turned on the display of "Icosahedron #3" that corresponds to this position.
Turning off the dsplay of the Jitterbug allows us to see the full Icosahedron. Note that 2 of the Icosahedron's vertices are at the green special positions.
To make it easy to stop the animation at the special positions, click on the "Pause at Poly. Pos." button. This turns off the animation. This means that to proceed to the next special position you need to click on the "Animation" button agian.
Here I show the Jitterbug in one of the Dodecahedra positions.
It is known that there are 5 cubes also defined by the vertices of a Dodecahedron. So this special blue Jitterbug position is also the position of a Cube. It is further known that 2 Tetrahedron share the same vertices of a Cube. So this position is also the position of Tetrahedra (not shown with this program).
If you click on the "Allow Intersecting" button, the triangular faces of the Jitterbug are allowed to pass through each other. As shown by the color coding of the special Jitterbug positions, there are also positions for the Dodecahedron/Cube?Tetrahedron, and the Icosahedron with intersecting Jitterbug triangles.
Displaying all 5 Jitterbugs at the same time shows the coordination of the Jitterbugs.
Clicking on the "Cylinders" button displays the 4 cylinders that Jitterbug #1 triangular faces rotate within. (I know the cylinders are hard to see.)
That's basically it. Have fun exploring the Jitterbug motion with the interactive web page!
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