... In view of the almost universal prevalence of the Pleiades year throughout the Polynesian area it is surprising to find that in the South Island and certain parts of the North Island of New Zealand and in the neighboring Chatham Islands, the year began with the new Moon after the yearly morning rising, not of the Pleiades, but of the star Rigel [*78] in Orion ...

... The Gilbert Islanders are Polynesians, having emigrated, according to their traditions, from Upolu, Samoa, which they look upon as te buto (Maori pito), the Navel of the World. They never counted the nights of the Moon beyond the twentieth, so far as Grimble was able to ascertain, and in the vagueness of their lunar calendar bore no resemblance to their Micronesian neighbors of the Carolines ... One of the names for east, Makai-oa, was said to be the name of a far eastern land, not an island, which their navigators had visited in ancient times. Tradition called this great land 'the containing wall of the sea, beyond the eastern horizon, a continous land spreading over north, south, and middle, having a marvelous store of all sorts of food, high mountains and rivers'. It was also called Maia-wa (wa being 'space, distant'). This is a clear reference to ancient voyages to the American coast from which the Polynesians are thought to have introduced the sweet potato into the Pacific area. The similarity of Maia to Maya may be more than a coincidence ...

But 26º S was at Antares and not at Rigel. For the declination of Rigel was 24º + 8 → 32º below that of the Pleiades.

Although the Mayas combined 20 with 13 we can interpret this as simply one half of a bicycle.

2 * 260 = 520 (→ 40 * 13). The other half would be the same and nothing of importance would thus be added by continuing through another round:

... When it was evident that the years lay ready to burst into life, everyone took hold of them, so that once more would start forth - once again - another (period of) fifty-two years. Then (the two cycles) might proceed to reach one hundred and four years. It was called One Age when twice they had made the round, when twice the times of binding the years had come together. Behold what was done when the years were bound - when was reached the time when they were to draw the new fire, when now its count was accomplished. First they put out fires everywhere in the country round. And the statues, hewn in either wood or stone, kept in each man's home and regarded as gods, were all cast into the water. Also (were) these (cast away) - the pestles and the (three) hearth stones (upon which the cooking pots rested); and everywhere there was much sweeping - there was sweeping very clear. Rubbish was thrown out; none lay in any of the houses ...

→ All numbers ought to be doubled and 2 * 52 = 104 = 4 * 26. The numbers displayed in the tresses of Pacha-mama (the World Mother) were in tune:

Counting the tresses from right to left:
1	26	78	1	29	90
2	26		2	30
3	26		3	31
4	25	104	4	34	124
5	26		5	31
6	27		6	30
7	26		7	29
Total = 396 = 182 + 214

Octo (as in October) means 8 and an Octopus has 8 limbs → 8º S for Rigel.