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This illustration of cosmos from the Chinese Turkestan is full of significant details. For our purpose at present, though, it is only necessary to count the days at the bottom.

There are 13 or 14 triangular forms, shaped like pyramids, below Spring. In the center and below the King there are 4 of these in full view:

 
Although my picture is blurred it is obvious each 'pyramid' is formed by 4 levels and 7 squares. Therefore we can count each of these 'pyramids' as a week. 13 * 7 = 91 corresponds to a quarter of 364 days. Adding twice 4 (for the only partially visible pyramids) makes 99.
 
At the top of the Tree I think there could be 3 more full weeks (although the first of them is partly hidden), but then there seems to be only the 4 steps up of the  top of the 4th pyramid. This is presumably where the King is making his sacrifice, where the Cloth is hiding what happens:

91 + 25 = 116 (= 4 * 29). If we should count from spring equinox (March 21), then the day number (according to the Gregorian calendar) will be 80 + 116 = 196, i.e. July 15.
 
Heka 5 6 (59) 7 8
July 13 14 15 (196) 16
Ca5-9 Ca5-10 Ca5-11 (116) Ca5-12
te hokohuki erua te marama te maitaki
no star listed Markab Puppis (114.7), Procyon (114.9) σ Gemini (115.7), Pollux (116.2) Azmidiske (117.4)
Heka 9 (63) 11 12
July 17 18 19 20 (201)
Ca5-13 Ca5-14 Ca5-15 (120) Ca5-16
te henua kua haga te mea ke manu puoko i tona ahi kua heu te huki
no stars listed Drus (119.9) Naos (121.3)
Ga2-18 Ga2-19 Ga2-20 Ga2-21 Ga2-22 Ga2-23 (54)
Gomeisa (111.6), ρ Gemini (112.1) Castor (113.4) no stars listed Markab (114.7), Procyon (114.9) σ Gemini (115.7), Pollux (116.2) Azmidiske (117.4)
July 11 12 (193) 13 14 15 16
Heka 3 4 5 6 (59) 7 8
Ga2-24 Ga2-25 Ga2-26 (*120)
 no stars listed  χ Carinae (119.9)
17 18 July 19 (200)
9 10 Heka 11 (64)

The top row of 8 arches, perhaps representing 8 * 29½ = 236 nights, could illustrate the extent of the front side of a whole lunar cycle with 472 nights. 

This does not mean 236 nights equals 116 days (the number of squares forming 'pyramids' of weeks in the bottom row). Instead, a more reasonable explanation is to say the presence of Sun is beginning 40 days after the March equinox. 80 + 40 + 116 = 236:

Hanga Takaure
An Nathra 5 6 7 8 (100)
August 21 22 23 24 (236)
Ca6-13 Ca6-14 Ca6-15 Ca6-16
manu teketeke ki ruga takaure kua aha te takaure i te henua ma te rima
Sadalmelik (334.6)      
 Regulus (152.7), λ Hydrae (153.2)  no star listed Simiram, Adhafera, Tania Borealis (154.7), Algieba (155.5) Tania Australis(156.0) 

Accordig to Wikipedia the Toltec culture had a pyramid with 4 levels: