Just over seven years ago, everybody suddenly stopped talking about the Maya people. It is time to rectify that!
For clarification, I am talking about the Mesoamerican Long Count Calendar. Your program will have as input a date in the Gregorian Calendar, and as output the corresponding date from the aforementioned Mesoamerican calendar.
That calendar counts days since August 11, 3114 BCE. It divides that number of days into periods of different lengths. There's the single day, the Winal (20 days), the Tun (18 Winal, or 360 days), the K'atun (20 Tun, 7200 days), and the B'ak'tun (20 K'atun, 144 000 days).
So you have your number of days since the epoch, then you find out how many of each period fit in there. Let's take William the Conqueror's coronation date of December 25, 1066. We're not bothering with the Julian Calendar here - we're using the Proleptic Gregorian Calendar for dates in the distant past (including the Maya epoch): basically the system of leap days every four years, except years divisible by 100 but not by 400, which I trust you're all familiar with.
Between Christmas Day in 1066 and the Maya epoch date of August 11, 3114 BCE, there's 1526484 days. In that number, you can fit 10 periods of 144000 days, so that's our B'ak'tun. The remainder, 86484, can fit 12 periods of 7200 days, so that's the K'atun. The remainder is 84. That's less than 360, so our Tun is 0. You can fit 4 Winal though, leaving a remainder of 4 days.
Now concatenate all those numbers with full stops in between, in decreasing order of period length. The date of 25 December 1066 becomes 10.12.0.4.4.
Your program will take as input a date in the Gregorian Calendar, between January 1, 1 AD (126.96.36.199.3), and 31 December, 3999 AD (188.8.131.52.6). The date can be in any format you want (my test cases will be using ISO 8601) as long as it is in the Gregorian calendar.
That means, valid input formats include (but are not limited to) "22 MAR 2233", "7/13/2305", "20200107T000000Z", and "2020-01-07T00:00:00+00:00", even an array like ", , ", depending on what your language parses the most easily or what approach you want to use. It is not allowed however to include any information beyond year, month, day of the month, time (has to be 00:00:00) and time zone (has to be GMT). Once I start allowing the day of the year, the Unix timestamp, a full-fledged DateTime data object (which contains a host of other values) or some other date tracking scheme, this issue would no longer be about converting a Gregorian date into a Mayan date, but only about representing a Mayan date. So basically, just stick with a primitive or a list of primitives for input.
It will output a string containing the corresponding Mayan date, as discussed above. It has to be a single string of numbers separated by periods; an int array is not allowed. Using a built-in Maya converter in your language (though I would be surprised if it had one) is not permitted either.
The question is tagged code-golf, so the shortest program in byte count wins!
Gregorian; Mayan 1-1-1; 184.108.40.206.3 1-1-2; 220.127.116.11.4 1066-12-25; 10.12.0.4.4 2000-2-29; 18.104.22.168.1 2012-12-21; 22.214.171.124.0 2020-1-5; 126.96.36.199.11 2100-3-1; 188.8.131.52.6 2154-4-11; 184.108.40.206.10 3999-12-31; 220.127.116.11.6