The Aztec Calendar
The calendar was not only central to religion in Mesoamerica, it was central to people's lives. Two separate calendars were observed, a solar calendar of 365 days (presumeably adjusted in leap years), and a Sacred Calendar, known as the Tonalpohualli of 260 days. The continuous sequence and the twenty signs are shown below:

 

Number Day-sign Glyph Ruled by Year
1 Cipactli (Water-monster) Tonacatecuhtli  
2 Ehecatl (Wind) Quetzalcoatl  
3 Calli (House) Tepeyollotl Year-name
4 Quetzpalin (Lizard) Huehuecoyotl  
5 Coatl (Snake) Chalchihuitlicue  
6 Miquiztli (Skull) Tecciztecatl  
7 Mazatl (Deer) Tlaloc  
8 Tochtli (Rabbit) Mayahuel Year-name
9 Atl (Water) Xiuhtecuhtli  
10 Itzcuintli (Dog) Mictlantecuhtli  
11 Ozomatli (Monkey) Xochipilli  
12 Malinalli (Grass) Patecatl  
13 Acatl (Reed) Tezcatlipoca Year-name
1 Ocelotl (Jaguar) Tlazolteotl  
2 Cuauhtli (Eagle) Xipe Totec  
3Cozcaquauhtli (Vulture) Itzpapalotl  
4 Ollin (Motion) Xolotl  
5 Tecpatl (Knife) Tezcatlipoca Year-name
6 Quiahuitl (Rain) Chantico  
7Xochitl (Flower) Xochiquetzal  
8 Cipactli (Water-monster) Tonacatecuhtli  

Since there are 20 signs and 13 numbers, any given day sequence will repeat every 13x20=260 days, hence the 260-day Sacred Calendar.
Only four of the signs, Calli, Tochtli, Acatl, and Tecpatl, can be the names of a year - a Solar Year. This is because a year is named for the first day in that year, and, since there is one Sacred Year + 105 days in a Solar Year, the sign of the first day will advance by 5 every year, meaning that only 20/5=4 of the day-signs can be year-names. The numbers are not evenly divisible, so any number can define a year.
The Solar Year is divided into eighteen months, each one twenty days long. Since there are twenty signs, each month of a given year begins on the same sign as the year. 18x20=360, which means 5 (or 6) days are left over to finish the year; these are known as the Nemotemi, the "Five Useless Days."

Now, just a little more arithmetic shows that, since only four of the signs can define a year but since all thirteen of the numbers can, the cycle you see moving above begins to repeat itself after 13x4=52 years, which was known as a "Bundle of Years." Such a bundle is defined as beginning in a year whose first day is Ome Acatl (Two Reed), which is why the number two, along with the year-signs Acatl, Tecpatl, Calli, and Tochtli, are shown in red in the moving graphic. Fifty-two years is also the amount of time it takes for Venus to make one complete cycle of its phases and positions relative to the earth and sun.