Talk:Schlegel diagram

Missing Discussion of Projection Distortions Associated W/Schlegel Diagram From 4D to 2D

Hello -

There are a number of misleading aspects of a Schlegel Diagram as it relates to tesseracts. The diagram is *accurate* but only to the degree that people are aware of the distortions. For example, a tesseract has *zero* outside faces. Each face attaches to an adjoining cube. For another, there is no "inside" cube, but rather a 4D void that is *bounded* by (8) 3D cubes. For yet another, no the larger "cube" does not count as the 8th cube. For still another, please understand that mathematically, this projection was built looking orthogonally directly down one axis. That means that two cubes are effectively super-imposed on one another. That "internal" cube is really 2 cubes bounding a 4D void on either side (as are the other 6 cubes, each pair in a different 3-brane). And for yet another, please understand that the six distorted side cubes do not have a face that creates the outer wall of the "Big Cube". No. Each of those side cubes (due to distortion) are actually concave regions: Both their "inner" and "outer" faces are super-imposed on top of each other--due to fact we are mathematically looking down axis in K Dimension. In other words, one of the faces attaches to one of the "inner" cubes and the other face attaches to the other cube.

So that boggles the mind, right? The Schlegel Diagram is *accurate* but by itself misleading.

I would offer another model--if people are interested in seeing it--that has its own distortion but of a different type, due to the mathematical viewing angle. As such, it clarifies the Schlegel Diagram and the Schlegel clarifies it. Together, they make it possible to comprehend tesseracts.

Why is this valuable? There are actually applications for tesseracts. It goes beyond the scope of this, but in a nutshell, one way is that it demonstrates a way to abstractly increase information density by many times...but only if people *understand* them.

To verify the veracity of this claim, one merely has to do the work. We are only talking about a small number of vertices from (0,0,0,0) to (1,1,1,1)--16. It is not that hard. The trick is to appreciate the multiple 3-branes--another assumption is that all 8 cubes are in (x,y,z). They are not. Two are in (x,y,z), two are in (x,y,k), two are in (y,z,k), and two are in, (x,z,k).

In the Exploded Schlegel Model, the 8 cubes are clearly visible surrounding a 4D void. They have no outside faces and each face is identified (with markup features) as adjoining an adjacent cube's face. There are clearly 6 ways to circumnavigate the tesseract. The inner 4D void symbolically has 8 in/out vectors (which would only be literal in-out vectors in 4D space). My sources are my own work.

LetMeHelp2019 (talk) 16:52, 18 October 2019 (UTC)

Ok, well have let this cook for a while. No responses yet. Will try an edit and see what people think. Thanks. LetMeHelp2019 (talk) 13:43, 6 January 2020 (UTC)

The opening sentence says it is a projection and distortion is necessary. Do you want some example animations of 3D rotations of 4D projected figures? Tom Ruen (talk) 15:36, 6 January 2020 (UTC)