| c1 = |
1
0
0 |
c2 = |
0
1
0 |
c3 = |
0
0
1 |
c4 = |
0
1
1 |
c5 = |
1
1
1 |
|
|
|
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.
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