Category:Face lattice of the tesseract (Bilinski)

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This image set can be scrolled interactively with the mouse (wheel or dragging). This is done by using the template Imagestack.
 See also category: Tesseract subspaces (image set).

The number of k-faces in the tesseract (0 ≤ k ≤ 4) is Sloane'sA038207(4, k). The total number is 34 = 81.
Based on their coordinates, these 81 points can be labelled with integers between −40 and 40. (This list shows the coordinates with positive values.)

k −1 0 1 2 3 4
number of k-faces 1 16 32 24 8 1
names empty face vertices edges (2-)faces cells 4-polytope

There are 216 links between centers of actual k-faces, starting with k=0. The complete face lattice also includes the empty face, and has 16 links from it to the vertices.

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vertices (red), edge centers (orange)
edge centers (orange), face centers (green)
face centers (green), cell centers (blue)
cell centers (blue), tesseract center (black)
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81 centers of k-faces (and 216 links between them)
k-faces labelled with integers
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negative
 
negative, origin, positive     (like this)
 
positive

POV-Ray source: Most images are rendered with face_lattice.pov. The labels file with labels.pov.

Pages in category "Face lattice of the tesseract (Bilinski)"

This category contains only the following page.