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 |
 |
Email: Mark Newbold mailto:mark@dogfeathers.com
This page URL: http://dogfeathers.com/java/hyperslice-3d.html