# Interactive Zonotope Viewer

This page is outdated! Please visit Online Zonotope Builder and Viewer.

Interactively view a zonotope in 3D space. The zonotope is generated by 5 vectors c1 ... c5. You may need a brief on zonotopes.

 c1 = 100 c2 = 010 c3 = 001 c4 = 01 1 c5 = 111

## Instructions

• Use the mouse to rotate and spin the zonotope
• The print button will save a screenshot as an eps-file
• The option bsp will enumerate the 12 faces
• Note that, by symmetry, each face has a translated counterpart
• Load the vertex and face definition for this zonozope.

## Remarks

• A Zonotop in 3D space as the Minkowski sum of n segments will have at most n*(n-1) faces. To see why, consider all n*(n-1)/2 pairs of segments, each pair generating a parallelogram. If non of these parallelograms lies in the same plane, then each of them will form two faces by symmetry. This is the proof of a corollary to a Theorem by Gritzmann and Sturmfels on the number of faces in Rd.
• However, the zonotope on this page does not have 5*4=20 faces. This is because the 3 pairs formed by c2, c3 and c4 are in the same plane, reducing the independent pairs from 10 to 8. The same is also true for the pairs formed by c1, c4 and c5. Therefore we only have (10-2-2)*2=12 faces.

Last modified by Wolfgang Kühn on Sunday, May 09, 2004