Category:Cube subspaces (image set)
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This category is an image set. It should contain only images that have the same style, and should have a parent category that is purely topical.
See also category: Tesseract subspaces (image set).
These are the sets of fixed points of permutations of the cube (see full octahedral group),
i.e. mainly its symmetry axes and mirror planes (plus the origin and the whole space as least and greatest elements).
Their total number is 24. That is entry 3 of A007405, the Dowling numbers.
Their number by dimension is row 3 of A039755, the B-analogs of Stirling numbers of the second kind.
3-dim. | 1 | 1 |
2-dim. | 3, 6 | 9 |
1-dim. | 3, 6, 4 | 13 |
0-dim. | 1 | 1 |
24 |
3 (cube) |
---|
1 ... 13 |
2a (squares) | 2b (rectangles) | |||||||
---|---|---|---|---|---|---|---|---|
0 1, 3, 2, 4 |
1 1, 9, 8, 10 |
2 3, 9, 6, 12 |
3 9, 4, 5, 13 |
2 9, 2, 7, 11 |
4 3, 10, 7, 13 |
1 3, 8, 5, 11 |
5 1, 12, 11, 13 |
0 1, 6, 5, 7 |
1a (axes) | 1b (square diagonals) | 1c (cube diagonals) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
2 9 |
1 3 |
0 1 |
0 2 |
1 4 |
2 8 |
3 10 |
4 6 |
5 12 |
3 13 |
2 11 |
1 7 |
0 5 |
0 (origin) |
---|
Subcategories
This category has the following 3 subcategories, out of 3 total.
C
Pages in category "Cube subspaces (image set)"
The following 2 pages are in this category, out of 2 total.
Media in category "Cube subspaces (image set)"
The following 31 files are in this category, out of 31 total.
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Cube diagonal lengths.png 3,919 × 1,295; 173 KB
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Cube subspace 0.png 2,000 × 2,000; 142 KB
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Cube subspace 1a0.png 2,000 × 2,000; 161 KB
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Cube subspace 1a1.png 2,000 × 2,000; 161 KB
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Cube subspace 1a2.png 2,000 × 2,000; 152 KB
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Cube subspace 1b0.png 2,000 × 2,000; 176 KB
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Cube subspace 1b1.png 2,000 × 2,000; 155 KB
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Cube subspace 1b2.png 2,000 × 2,000; 181 KB
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Cube subspace 1b3.png 2,000 × 2,000; 181 KB
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Cube subspace 1b4.png 2,000 × 2,000; 161 KB
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Cube subspace 1b5.png 2,000 × 2,000; 186 KB
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Cube subspace 1c0.png 2,000 × 2,000; 180 KB
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Cube subspace 1c1.png 2,000 × 2,000; 159 KB
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Cube subspace 1c2.png 2,000 × 2,000; 230 KB
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Cube subspace 1c3.png 2,000 × 2,000; 161 KB
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Cube subspace 2a0.png 2,000 × 2,000; 219 KB
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Cube subspace 2a1.png 2,000 × 2,000; 206 KB
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Cube subspace 2a2.png 2,000 × 2,000; 188 KB
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Cube subspace 2b0.png 2,000 × 2,000; 199 KB
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Cube subspace 2b1.png 2,000 × 2,000; 277 KB
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Cube subspace 2b2.png 2,000 × 2,000; 242 KB
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Cube subspace 2b3.png 2,000 × 2,000; 201 KB
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Cube subspace 2b4.png 2,000 × 2,000; 274 KB
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Cube subspace 2b5.png 2,000 × 2,000; 268 KB
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Cube subspace 3.png 2,000 × 2,000; 153 KB
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Cube subspaces Hasse matrix.svg 5,906 × 8,156; 95 KB
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Hypercube subspace 1a, edge 1.png 1,669 × 306; 29 KB
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Hypercube subspace 1b, edge sqrt(2).png 2,234 × 306; 19 KB
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Hypercube subspace 1c, edge sqrt(3).png 2,662 × 305; 32 KB
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Hypercube subspace 2a, square 1.png 1,669 × 1,667; 47 KB
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Hypercube subspace 2b, rect 1 by sqrt(2).png 2,232 × 1,669; 77 KB