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 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's A007405, the Dowling numbers.
Their number by dimension is row 3 of Sloane's 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)


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.

C

Pages in category "Cube subspaces (image set)"

The following 2 pages are in this category, out of 2 total.

C

Media in category "Cube subspaces (image set)"

The following 31 files are in this category, out of 31 total.

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