The 3 Aztec calendars
Aztec astrology is a complex science that uses 3 different calendars:
- Tonalpohualli
- Xiuitl
- The Secular calendar – defined by the Sun, Moon and Venus.
Tonalpohualli astrology, a sacred divination calendar composed of 260 days.
This system defines periods of 13 days (in the manner of our weeks), to which 20 signs are associated (20 x 13 = 260). Each day is therefore designated by the association of a sign, or glyph, and a figure between 1 and 13, which in turn is associated with a divinity. Certain days can be considered as beneficial or harmful according to the number with which they are associated. This calendar serves to predict the future and the destiny of each one according to his or her day of birth.
Xiuitl, a solar calendar of 365 days
The days are grouped, not in 12 lunar months, but in 18 months of 20 days, to which are added 5 days in which the god Nemomtoni or Nemotemi is worshipped. On the twentieth day of each month, and therefore 18 times a year, are celebrated their festivals, during which they proceed to human sacrifices for the salvation of the Earth, according to Aztec belief.
Ximolpilli or the Aztec Century
These calendars are in turn part of a longer cycle of 52 years, called Ximolpilli or the Aztec Century, divided into four periods of 13 years, corresponding to the 13 periods of the divinatory calendar. Each of these periods is associated with a figure and a sign, from among the following: Acatl (reed), Tecpatl (flint), Calli (house), Tochtli (rabbit). Because of this cycle, two people born on the same day 52 years apart will have the same sign.

This agreement of the number and the sign of the 52 years is called the "League of the years", the moment in which the Aztecs celebrate the Festival of the New Fire.
The fact that a man who reaches the age of 52 officially enters old age is also noteworthy, it's a symbol of respect and the reason why he is relieved of many obligations such as paying for his rights. His judgment is taken into account, and at that moment he is allowed to drink pulque, a fermented drink based on pita.
Técpatl is rather referring to obsidian than flint; I´d say.
MS, 6 years ago
Tecpatl = Flint, Obsidian = Itztli
Richie, 3 years ago