![]() ![]() They stay in the same place just spinning around like the two side faces of the cube in the 3D to 2D projection. Now take a look at the cells around the side. When you can visualize it that way, you are doing it right. Try to visualize the red cell swinging out in front, around the side, around the back and out in front again. You need to remember that when the red cell looks like the smaller center cube, its really in the back, and when the red cell looks like the big "outer" cube, its really in front. If you are visualizing it as turning inside out, you are only seeing the projected image. ![]() Now, with that in mind, look at this XW hypercube rotation, watching the red cell of the hypercube. If you visualize the projected image on the plane as "turning inside out", then you are merely visualizing the projected image and not reconstructing the original object. Recognize that when we mentally reconstruct the cube from its projected image, we do not see the smaller square as being inside the larger one, but behind it. It is a little harder now to see the image as being stricly in a plane, and it is easier to visualize the faces of the projected cube in a 3D space. Now, look at this animation, with the yellow points connected accordingly. ![]() Watch how in the plane the smaller middle square seems to turn inside out, moving outside the center, around the sides, and back in the opposite side. Try to restrict your imagination to only the yellow points on the plane. First, take a look at this 3-D to 2-D animation. Through analogy, we shall determine the more correct one. There are two ways to look at these animations. Interpreting The Hypercube Rotation Projection Here is how the writing on the page appeared: It's unfortunate that the link is no longer available for some reason, but it was a good thing that I copied the webpage in case that happened. That was interesting Hugh but the link failed. ![]()
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