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The mayan calendar

The site webexhibits.org/calendars/calendar-mayan.html has a beautiful picture of an Aztec calendar and the temple of El Castillo, at Chichen-Itza. This is how they explain the Mayan calendar.
Among their other accomplishments, the ancient Mayas invented a calendar of remarkable accuracy and complexity. At right is the ancient Mayan Pyramid Chichen Itza, Yucatan, Mexico. The Pyramid of Kukulkan at Chichén Itzá, constructed circa 1050 was built during the late Mayan period, when Toltecs from Tula became politically powerful. The pyramid was used as a calendar: four stairways, each with 91 steps and a platform at the top, making a total of 365, equivalent to the number of days in a calendar year.

The Maya calendar was adopted by the other Mesoamerican nations, such as the Aztecs and the Toltec, which adopted the mechanics of the calendar unaltered but changed the names of the days of the week and the months. The Maya calendar uses three different dating systems in parallel, the Long Count, the Tzolkin (divine calendar), and the Haab (civil calendar). Of these, only the Haab has a direct relationship to the length of the year. A typical Mayan date looks like this: 12.18.16.2.6, 3 Cimi 4 Zotz. 12.18.16.2.6 is the Long Count date. 3 Cimi is the Tzolkin date. 4 Zotz is the Haab date.
The Long Count is really a mixed base-20/base-18 representation of a number, representing the number of days since the start of the Mayan era. It is thus akin to the Julian Day Number. The basic unit is the kin (day), which is the last component of the Long Count. Going from right to left the remaining components are: uinal(1 uinal = 20 kin = 20 days), tun(1 tun = 18 uinal = 360 days = approx. 1 year), katun(1 katun = 20 tun = 7,200 days = approx. 20 years), and baktun(1 baktun = 20 katun = 144,000 days = approx. 394 years). The kin, tun, and katun are numbered from 0 to 19. The uinal are numbered from 0 to 17. The baktun are numbered from 1 to 13.

Mayan ceramics