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.
These images use the same colors and numbers as the corresponding set for the tesseract (left). But there are also versions in plain gray (right).

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 Sloane'sA007405, the Dowling numbers.
Their number by dimension is row 3 of Sloane'sA039755, 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)
Cube subspace 3.png
1 ... 13
2a (squares) 2b (rectangles)
0
Cube subspace 2a0.png
1, 3, 2, 4
1
Cube subspace 2a1.png
1, 9, 8, 10
2
Cube subspace 2a2.png
3, 9, 6, 12
3
Cube subspace 2b3.png
9, 4, 5, 13
2
Cube subspace 2b2.png
9, 2, 7, 11
4
Cube subspace 2b4.png
3, 10, 7, 13
1
Cube subspace 2b1.png
3, 8, 5, 11
5
Cube subspace 2b5.png
1, 12, 11, 13
0
Cube subspace 2b0.png
1, 6, 5, 7
1a (axes) 1b (square diagonals) 1c (cube diagonals)
2
Cube subspace 1a2.png
9
1
Cube subspace 1a1.png
3
0
Cube subspace 1a0.png
1
0
Cube subspace 1b0.png
2
1
Cube subspace 1b1.png
4
2
Cube subspace 1b2.png
8
3
Cube subspace 1b3.png
10
4
Cube subspace 1b4.png
6
5
Cube subspace 1b5.png
12
3
Cube subspace 1c3.png
13
2
Cube subspace 1c2.png
11
1
Cube subspace 1c1.png
7
0
Cube subspace 1c0.png
5
0 (origin)
Cube subspace 0.png


Cube face centers and their integer values from −13 to 13
Subspaces of rank 1 in those with rank 2

Subcategories

This category has the following 3 subcategories, out of 3 total.

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.