The diagram shows how astronomical facts (equinoxes, solstices and zenith passages of the sun) forced a structure for the year (haab) which is 105 (= 52½ + 52½) + 260 (= 180 + 40 + 40) days. That was the situation at the latitude of Copan.
vernal equinox - zenith passage 2 uinal
zenith passage - summer solstice 52½ kin
summer solstice - zenith passage 52½ kin
zenith passage - autumn equinox 2 uinal
autumn equinox - vernal equinox 9 uinal
total 1 haab

(Skywatchers)

So perhaps the 260 kin period (tzolkin) derives from this rather than from some mystic idea of 13 * 20?

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