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 
A038207(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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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.
Media in category "Face lattice of the tesseract (Bilinski)"
The following 11 files are in this category, out of 11 total.
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Edges in the face lattice of the tesseract, rank 0 to 1.png 2,592 × 3,600; 1.37 MB
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Edges in the face lattice of the tesseract, rank 1 to 2 (4 cubes).png 2,592 × 3,600; 1.48 MB
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Edges in the face lattice of the tesseract, rank 2 to 3 (6 squares).png 2,592 × 3,600; 723 KB
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Edges in the face lattice of the tesseract, rank 3 to 4 (4 line segments).png 2,592 × 3,600; 160 KB
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Face lattice of the tesseract, labels.png 2,592 × 3,600; 1.38 MB
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Face lattice of the tesseract.png 2,592 × 3,600; 2.86 MB
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Layers in the face lattice of the tesseract, 1 (L).png 2,592 × 3,600; 962 KB
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Layers in the face lattice of the tesseract, 2 (LM).png 2,592 × 3,600; 636 KB
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Layers in the face lattice of the tesseract, 3 (M).png 2,592 × 3,600; 839 KB
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Layers in the face lattice of the tesseract, 4 (MR).png 2,592 × 3,600; 646 KB
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Layers in the face lattice of the tesseract, 5 (R).png 2,592 × 3,600; 995 KB