3-bit Walsh permutation/ortho

The subpage .../comet shows the same information in a different layout.

19 different shapes

Contents

60 based on 12 squares

12 squares

24 simple parallelograms of type 1

24 simple parallelograms of type 2

48 based on 12 rectangles

12 rectangles

12 wide parallelograms (type 1)

12 long parallelograms (type 1)

12 hexagons (type 2)

144 based on 24 rectangles

24 rectangles

24 wide parallelograms (type 2)

48 long parallelograms (types 1 and 2)

48 hexagons (types 1 and 2)

There are 252 different orthographic projections. They form 63 groups of four, that look similar. They are all shown below.
Within such a group, each image has a reflection at the antidiagonal and an image with the same outline.

Some images also have horizontally or vertically mirrored equivalents. And a few have all eight rotations and reflections in the symmetry group of the square.
(These are all in the third section. The former in 24 rectangles and 48 long parallelograms, the latter in 48 hexagons.)

rect h rect h par long 1h par long 2h

par long 2v rect v par long 1v rect v

hex 2b hex 1b hex 1a hex 2a

hex 2a hex 1a hex 1b hex 2b

60 based on 12 squares

12 squares
100 yz xz xy axis + axis − yz xz xy axis + axis − 010 yz xz xy axis + axis − yz xz xy axis + axis − 001 yz xz xy axis + axis − yz xz xy axis + axis −

24 simple parallelograms of type 1

100 yz xz xy det. + (axis +) det. − (axis −) yz xz xy det. − (axis +) det. + (axis −) 100 yz xz xy det. + (axis +) det. − (axis −) yz xz xy det. − (axis +) det. + (axis −) 010 yz xz xy det. + (axis +) det. − (axis −) yz xz xy det. − (axis +) det. + (axis −) 010 yz xz xy det. + (axis +) det. − (axis −) yz xz xy det. − (axis +) det. + (axis −) 001 yz xz xy det. + (axis +) det. − (axis −) yz xz xy det. − (axis +) det. + (axis −) 001 yz xz xy det. + (axis +) det. − (axis −) yz xz xy det. − (axis +) det. + (axis −)

24 simple parallelograms of type 2

100 yz xz xy det. + (axis +) det. − (axis −) yz xz xy det. − (axis +) det. + (axis −) 100 yz xz xy det. + (axis +) det. − (axis −) yz xz xy det. − (axis +) det. + (axis −) 010 yz xz xy det. + (axis +) det. − (axis −) yz xz xy det. − (axis +) det. + (axis −) 010 yz xz xy det. + (axis +) det. − (axis −) yz xz xy det. − (axis +) det. + (axis −) 001 yz xz xy det. + (axis +) det. − (axis −) yz xz xy det. − (axis +) det. + (axis −) 001 yz xz xy det. + (axis +) det. − (axis −) yz xz xy det. − (axis +) det. + (axis −)

48 based on 12 rectangles

12 rectangles
110 yz xz xy det. + det. − yz xz xy det. − det. + 101 yz xz xy det. + det. − yz xz xy det. − det. + 011 yz xz xy det. + det. − yz xz xy det. − det. +

12 wide parallelograms (type 1)
110 yz xz xy det. + det. − yz xz xy det. − det. + 101 yz xz xy det. + det. − yz xz xy det. − det. + 011 yz xz xy det. + det. − yz xz xy det. − det. +

12 long parallelograms (type 1)
110 yz xz xy det. + det. − yz xz xy det. − det. + 101 yz xz xy det. + det. − yz xz xy det. − det. + 011 yz xz xy det. + det. − yz xz xy det. − det. +

12 hexagons (type 2)
!.. yz xz xy det. + (hex 2b) det. − (hex 2a) yz xz xy det. − (hex 2b) det. + (hex 2a) .!. yz xz xy det. + (hex 2b) det. − (hex 2a) yz xz xy det. − (hex 2b) det. + (hex 2a) ..! yz xz xy det. + (hex 2b) det. − (hex 2a) yz xz xy det. − (hex 2b) det. + (hex 2a)

144 based on 24 rectangles

24 rectangles
110 foo yz xz xy axis + axis − yz xz xy axis + axis − bar yz xz xy axis + axis − yz xz xy axis + axis − 101 foo yz xz xy axis + axis − yz xz xy axis + axis − bar yz xz xy axis + axis − yz xz xy axis + axis − 011 foo yz xz xy axis + axis − yz xz xy axis + axis − bar yz xz xy axis + axis − yz xz xy axis + axis −

24 wide parallelograms (type 2)
110 foo yz xz xy axis + axis − yz xz xy axis + axis − 110 bar yz xz xy axis + axis − yz xz xy axis + axis − 101 foo yz xz xy axis + axis − yz xz xy axis + axis − 101 bar yz xz xy axis + axis − yz xz xy axis + axis − 011 foo yz xz xy axis + axis − yz xz xy axis + axis − 011 bar yz xz xy axis + axis − yz xz xy axis + axis −

48 long parallelograms (types 1 and 2)

110 < type 1   foo yz xz xy axis + axis − yz xz xy axis + axis − type 2   bar yz xz xy axis + axis − yz xz xy axis + axis − 110 > type 2   foo yz xz xy axis + axis − yz xz xy axis + axis − type 1   bar yz xz xy axis + axis − yz xz xy axis + axis − 101 < type 1   foo yz xz xy axis + axis − yz xz xy axis + axis − type 2   bar yz xz xy axis + axis − yz xz xy axis + axis − 101 > type 2   foo yz xz xy axis + axis − yz xz xy axis + axis − type 1   bar yz xz xy axis + axis − yz xz xy axis + axis − 011 < type 1   foo yz xz xy axis + axis − yz xz xy axis + axis − type 2   bar yz xz xy axis + axis − yz xz xy axis + axis − 011 > type 2   foo yz xz xy axis + axis − yz xz xy axis + axis − type 1   bar yz xz xy axis + axis − yz xz xy axis + axis −

48 hexagons (types 1 and 2)

!.. type 1   spam yz xz xy axis + (hex 1b) axis − (hex 1a) yz xz xy axis + (hex 1a) axis − (hex 1b) type 1   eggs yz xz xy axis + (hex 1b) axis − (hex 1a) yz xz xy axis + (hex 1a) axis − (hex 1b) type 2   spam yz xz xy axis + (hex 2b) axis − (hex 2a) yz xz xy axis + (hex 2b) axis − (hex 2a) type 2   eggs yz xz xy axis + (hex 2a) axis − (hex 2b) yz xz xy axis + (hex 2a) axis − (hex 2b) .!. type 1   spam yz xz xy axis + (hex 1b) axis − (hex 1a) yz xz xy axis + (hex 1a) axis − (hex 1b) type 1   eggs yz xz xy axis + (hex 1b) axis − (hex 1a) yz xz xy axis + (hex 1a) axis − (hex 1b) type 2   spam yz xz xy axis + (hex 2b) axis − (hex 2a) yz xz xy axis + (hex 2b) axis − (hex 2a) type 2   eggs yz xz xy axis + (hex 2a) axis − (hex 2b) yz xz xy axis + (hex 2a) axis − (hex 2b) ..! type 1   spam yz xz xy axis + (hex 1b) axis − (hex 1a) yz xz xy axis + (hex 1a) axis − (hex 1b) type 1   eggs yz xz xy axis + (hex 1b) axis − (hex 1a) yz xz xy axis + (hex 1a) axis − (hex 1b) type 2   spam yz xz xy axis + (hex 2b) axis − (hex 2a) yz xz xy axis + (hex 2b) axis − (hex 2a) type 2   eggs yz xz xy axis + (hex 2a) axis − (hex 2b) yz xz xy axis + (hex 2a) axis − (hex 2b)