Category:Cube subspaces (black in gray)

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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.
There are also the four hexagonal cross sections in the same style, but they are not symmetry planes.

These are the Sloane's A007405(3) = 24 different sets of fixed points of permutations of the cube (full octahedral group).
Those are mainly its symmetry axes and mirror planes. (Plus the origin and the whole space as least and greatest elements.)

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

Created with POV-Ray. See source: https://pastebin.com/tMK5TtzJ

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H

Pages in category "Cube subspaces (black in gray)"

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Media in category "Cube subspaces (black in gray)"

The following 24 files are in this category, out of 24 total.

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