Although the fishes with head up (waxing) and head down (waning) divide the 8 periods in the middle, with 4 periods for each phase, there is another structure hidden in the calendar, a structure which divides the 8 periods into 3 groups: waxing moon, full moon and waning moon.

The calendar has 72 glyphs, 36 up to full moon and 36 beyond full moon. A closer investigation reveals, however, another distribution:

We recognize these numbers (28 + 18 + 26 = 72). For example: The central 18 is a number which coincides with how period 18 in the G calendar for the year ends 'summer'. 28 is the number of glyphs in the first quarter of the K calendar for the year. 26 is the number of glyphs in the last (24th) period of the E calendar for the year.

Numbers alone are, though, not enough as proof. Therefore we need to look for confirmation at the signs in the glyphs too.