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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This page URL: http://dogfeathers.com/java/hyperslice-3d.html