If you search “Maya calendar” on Google you will see images of the Aztec calendar stone. The reason why this non-Maya monument has become the symbol for the Maya “end date” is understandable only from taking a look at the history of the 2012-phenomenon. As Whitesides and Hoopes writes, it was the Mayanist Michael Coe (1966) who related the 13 baktun “cycle” with that of the Aztec 5 Suns. This, in combination with Goodman’s (1897) earlier assertion that the Long Count was cyclical and the cycles of creations in Postclassic Maya sources like Popol Vuh, have laid the foundation for a belief, both among academics and 2012ers, that the Late Formative and Classic period Long Count calendar will end at 13 baktun and restart again. However, there are monuments, such as Stela 10 at Tikal, that inserts the five units Long Count in greater temporal contexts and there are no indications that there is a change at 13 baktun. Distance numbers also indicate the lack of a break at 13 baktun. For example, one of the astronomical tables at Xultun contains a time period of 17 baktuns. In fact, apart from a few “pre-era” dates (recorded as if they were part of another 13 baktun cycle), there are no records of dates from an era preceding the one supposedly preceding this one (which would be the case if the Classic period Maya believed in several World Ages).
What happened in the Postclassic Maya area was the emergence of the Short Count, a cycle of 13 katuns. These cycles would end and start all over again. During this period the Maya area became more “international”, being more influenced by Central Mexican ideas, ideas that likely arrived already during the Classic period when Teotihuacan played a substantial role in Early Classic Maya politics. However, as long as the divine kingship (ajawlel) was in existence this earlier influence did not affect the already established Long Count. With the collapse of Teotihuacan and the later Maya collapse, in combination with the earlier Late Formative collapse, ideas of cycles of history, World Ages if you want, got foothold in the Maya area as well. Hence, we must remember that Popol Vuh and the Five Suns mythology are from the same time period (Late Postclassic/Early Colonial periods), and they were the result of over two thousand years of waxing and waning of political systems and the calendars they utilized.
There are other reasons why the Five Suns mythology is incompatible with the Long Count as it is perceived by many 2012ers. In the 2012-mythology it is believed that the Five Suns are the same as Five 13 baktuns because this equals 25,675 years which is close to the length of the precession of the equinoxes (a Platonic Year), which is roughly 25,800 years. This is an idea promoted by Frank Waters (1975) and more recently by John Major Jenkins and other New Agers. However, for this model to work all five Long Counts must have the same length (13 baktuns). Is that the case for the Aztec Five Suns? Nope.
According to Miguel Leon-Portilla (1982) the first Sun (4-Ocelotl) began 2513 years before 1558. This would be 955 BC (long after the Long Count began). This Sun lasted for 676 years (this is 13 x 52 years). The second Sun (4-Ehecatl) lasted for 364 years (7 x 52 years). The third Sun (4-Quiahuitl) lasted for 312 years (6 x 52 years). The fourth Sun (4-Atl) lasted for 676 years (13 x 52 years). In-between the fourth and the current fifth Sun (4-Ollin) there is also supposed to be a transitional period of 2 x 13 years. There is no recorded “end date” for the fifth Sun but the next time it might end is October 2, 2027.
Now, although 13 is common in the Five Suns mythology, as 13 is an important number in the Maya Long Count, the Aztecs include two Suns with multiples of 7 and 6 (13 combined) and at least one transitional period. This is not even compatible with Jenkins and other 2012ers conceptualization of the Long Count where there are no transitional periods. Further, Jenkins argues that five 13 baktuns equals one cycle whereas Goodman argued for a cycle of 73 baktuns. 73 divided by 5 does not even give us an even number and hence the Jenkins/Waters cycles are incompatible with the numerical cycles Goodman sees in the structure of the calendar. However, in my view both cyclical views of the Long Count are wrong.