Slice draws 3-dimensional slices through the regular 4-dimensional polytopes, as they rotate. By clicking on the applet, you can view each of the six regular polytopes. These are:

In some cases, so long as the slice is generic (that is, it lacks any special alignment with the polytope’s features), the number of faces with various numbers of sides in the polyhedron obtained will be the same:

In other cases, there are multiple possibilities:

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Applets Gallery / Slice / created Monday, 11 March 2002
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Copyright © Greg Egan, 2002. All rights reserved.