Many hexagram lines have a mirror now, you find it below the lines in each hexagram.
This diagram (without the red line) comes from a paper by Edward Hacker and Steve Moore – 'A brief note on the two-part division of the received order of the hexagrams in the Zhouyi' published in the June 2003 issue of the Journal of Chinese Philosophy (30:2, pp 219–221). They discovered a diagram showing their idea was known in the Yuan (Mongol) dynasty. See http://biroco.com/division.htm
It seems to solve the mystery of the division of the hexagrams in two unequal parts (the 'upper' canon of 30 and 'lower' of 34 hexagrams). The hexagrams have the hexagram name written at one side, and the name of its inverted one upside down on the other side (I rotated the diagram 90°). So a hexagram, which does not change when inverted, should have on both sides the same name. In the diagram these double names are left blank (eg lower left corner).
For the 'mirrors' or line pathways it explains the relation of e.g. hex.3 line 2 with hex.4 line 5 (third hex. at left) and with hex.59 line 5 and 60 line 2. Hex.3 line 2 is fan-yao of hex.60 line 2 (when 3.2 changes, 60.2 corresponds with 3.2), and qian-yao with hex.4 line 5 (hex.3 upside down is hex.4, line 3.2 becomes 4.5).
To find the Mirror grouping for a specific line: go to its hexagram, and click on the Mirror of this line.
An example, Mirror grouping 33.2-44.2-43.5-34.5
What about hexagrams which do not change when upside down, like hex.2:
The paired hexagram of hex.2 is hex.2, because upside down is it still hex.2. What changes is the line: now it is line 4.
Mirror 2.3-15.3 This is an image of the line pathway starting at hex.2 line 3. Hex.2 is at the top left, with line 3 changing. Bottom left its fanyao 15.3. Bottom right hex.2, line 4 changing, above it its fanyao 16.4. If you rotate the image 90° clock- or counterclock-wise makes no difference. See below.
Another way to draw the image:
this is the same Mirror Grouping 2.3-15.3-2.4-16.4
but now with the qianyao side by side and the fanyao above-below.
Every Mirror grouping has a theme, depending on the lines and hexagrams involved. In the first example above, 33.2, the theme was how to deal with "possessing".
The theme of the mirror grouping of 2.3 is, that everything essential you do comes from your heart, not from what your brain wants. Wanting is limited and gives small results, following your heart or 'guts' is big. This kind of strong intention can cause ripples in space-time.
Heartfelt motivation attracts others (16.4)
you act from out your heart, not towards a result (2.3)
in cooperation, you give all of yourself (15.3)
when your heart is silent, you are silent (2.4)