The Maya counted the days by fives, thirteens and twenties. They gave numbers from 1 up to 13 to series of 20 day names in a continuous cycle. Maya world cube shows 4 points for each heaven and underworld, and 5 points for the earth's surface.

The numbers 4 and 5 are the basic numbers of Maya cosmology because they provide: 4 + 5 = 9; and, 4 + 5 + 4 = 13. These numbers play an important role in the functioning of the gods placed in those points following the calendar day names in a continuous cycle. Hear the Mayan Days in the Mayan language. These thirteens are found in Mayan cycles which are multiples of 13, for example, 26, 52, 65, 78 etc.

It is not easy to discover the real origin of the 13-day cycle.  The Maya considered the shape of their world as an enormous cube, or perhaps as a double pyramid divided to the four directions of the world.  The YAXCHé is the world tree which forms the axis and center of that world. YAX means "first", "new" or "green" (green-blue, blue), and -CHé generally means tree. Therefore meaning of yaxché is "first tree".  The Yaxché tree had 4 horizontal root branches leading to the 4 quarters of the world.  These points are the locations of the Bacabs.

Heaven is the high residence of the various gods.  The Bacabs are the Gods (and brothers)  Creator placed at the four points of the heavens to hold up the sky.  

 Mayan years correspond to the Bacabs the years along with the corresponding allocated gods

Year Bacab name Quarter Color
Kan Kanal-Bacab south yellow
Muluc Chacal-Bacab east red
Ix Sacal-Bacab north white
Cauac Ekel-Bacab west black

The underworld is the part of the Yaxché tree stump that's  underground.

The Mayan's had two calendar systems; one was the Tzolkin, a Sacred Almanac of 260 days. The other is in multiples of 18 that represents our 365 day astronomical calendar.

resources: http://users.skynet.be/fa039055/13days.htm

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