Schlegel Diagrams

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MBRosenberg
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Joined: Fri Jun 20, 2008 8:54 pm

Schlegel Diagrams

Post by MBRosenberg » Fri Jun 20, 2008 9:16 pm

Is there a feature of 4D Stella that allows the user to see the Schlegel digram of a particular 4D model? If so, can the user shift which cell is centered in the diagram, possibly by highlighting a cell and simply moving it with the mouse? If that were possible, I think it would be cool to select the cell, move it with the mouse, and release the button to send the cell from the inside of the Schlegel diagram to the side to the outside to the other side and back to the inside again, similar to how one can rotate a polyhedron and keep it spinning. And lastly, the main reason for this post is: Would it be possible to create a feature, if there isn't one already, that allows the user to morph a 4D model between its 3D net and its 3D Schlegel diagram? I think this feature would help users visualize how the 3D net of a 4D model can fold into the actual model. Furthermore, maybe the feature could allow the user to choose which cell of the 3D net will remain the center of the Schlegel diagram. And on top of that, maybe there could exist an equivalent function that changes a 2D net into a 2D Schlegel Diagram, and the user could choose which face of the net is the center.

If any of these features already exist, how does one access them?

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robertw
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Post by robertw » Sat Jun 21, 2008 4:46 pm

Schlegel diagrams are not directly supported as such, but they are really just extreme perspective projections, which are already possible. When you view the 120-cell in Stella4D, it should already have this appearance be default. For some more complex polytopes a more extreme perspective is required. This can be adjusted by entering 4D Tumble mode (Image), holding down Space, and Right-button-dragging the mouse.

You can then rotate the model in 4D to get the effect you want, which would appear to move the inner cell out to the outer and then back in the other side. For that, again in 4D Tumble mode, point the mouse at the cell of interest, hold down Ctrl and the left mouse button and drag. If you release while still dragging it should keep rotating on its own. Should look like this from the Stella home page
Image

Regarding folding up the 3D nets to the completed 4D model with a perspective projection back into 3D, it's on the to-do list, but probably won't happen for a while. Yes, it would be nice.

Rob.

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