A 3-Dimensional Analogy to HyperSpace Polytope Slicing
This web page was created as an aid to understanding
the HyperSlice Java applet, which displays
3-dimensional slices of 4-dimensional convex polytopes. It is equally relevant to the
newer HyperStar Java applet.
In the images (below), a polytope (a cube) is dragged vertex-first across
a lower-dimensional space (the gray
plane). The (flat) inhabitants of the lower-dimensional space see a continuously-changing
polytope in their space (a blue polygon which represents the intersection of the
cube with the gray plane).
The W value is the distance by which the higher-dimensional polytope is shifted
relative to the lower-dimensional space. In the HyperSlice
applet, this is controlled by the W-Slider control. In the HyperStar applet,
this is controled by the Section Slider control.
|W= -0.8 ||Slice = Small Triangle|
|W= -0.4 ||Slice = Large Triangle|
|W= 0.0 ||Slice = Hexagon|
|W= 0.4 ||Slice = Large Triangle|
|W= 0.8 ||Slice = Small Triangle|
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