73 (= 365 / 5) is a truly interesting number. It is connected with the pentagram and the planet Venus:
"The Mayan Venus calendar is best known from a table in the Dresden Codex (Thompson 1972:62-71), but the presence of Venus reckoning in the Guatemalan highlands is attested by the PV and by a Quiché almanac dating from 1722 (Berendt n.d.). A given Venus synodic period (lasting 584 days) is divided into four stages, with Venus appearing as the morning star at the beginning of the first stage and remaining visible throughout it (236 days or 8 synodic moons).

During the second stage (90 days), Venus goes through its last 27 days (one sidereal moon) as the morning star, disappears for 50 days, and runs through its first 13 days as the evening star. It remains visible as the evening star thoughout the third period (250 days) and stays out of sight throughout the fourth period (8 days), after which it returns to the first stage.

During a given 584-day period the 20 day names repeat 29 times, giving 580 days with a remainder of 4; this means that a Venus cycle will always begin 4 days later in the sequence of 20 day names than the previous cycle.

And since 20 is evenly divisible by 4 (20 / 4 = 5), only 5 of the day names can ever begin a Venus cycle. In the Dresden Codex the chosen days (here given their Quiché names) were Junajpu, K'at, Q'anil, E, and Ajmak, followed by Junajpu again.

Starting from 1 Junajpu (as the Dresden Codex does) and running through five complete periods so as to show all of the possible day names, the beginning dates for the four stages within each Venus period work out as follows:

DATES FOR FIVE SUCCESSIVE VENUS PERIODS
  First Second Third Fourth Fifth
Appearing as morning star: 1 Junajpu 13 K'at 12 Q'anil 11 E 10 Ajmak
Becomes invisible: 3 Ajmak 2 Junajpu 1 K'at 13 Q'anil 12 E
Appears as evening star: 2 Kame 1 Tz'i' 13 Ix 12 Tijax 11 Iq'
Becomes invisible: 5 Ajmak 4 Junajpu 3 K'at 2 Q'anil 1 E

After five complete cycles totaling 2,920 days, the movement of Venus fill eight idealized years of 365 days each and come within hours of spanning 99 lunations. At this point Venus begins repeating the same series of period-beginning day names but with different numbers, while at the same time coming very close to repeating its relationship to the fixed stars and the seasons of the solar year. To get back to a morning star appearance on 1 Junajpu, Venus must repeat the full set of five periods a total of thirteen times." (Popol Vuh)