The soleá is sung slowly and gravely, usually to one guitar, and its compás is the one many flamenco players learn to count first. Several other palos take their cycle from it — the alegrías and the bulerías on this site among them — which is why it is sometimes called the mother of the palos, though it is not the oldest of them.
Reading the cycle
The grid above is the cycle in the order its source prints it, from 1 to 12, with the five accented counts marked. Printed that way, each accent closes a group: the counts run three, three, two, two, two, with the strong count at the end of each group. Laid out from 12 instead, the same accents open the groups, and the table reads them from there. Nothing about the cycle changes between the two; only where you start saying the numbers.
The table then sets the soleá’s own grouping beside the two even ways of counting twelve. Counted in threes, the cycle puts downbeats on 12, 3 and 6, and misses 8 and 10. Counted in twos, it catches 12 and every accent in the second half, and misses the one on 3. Neither even count explains every accent on its own, but between them they explain all five: the first half of the cycle is counted in threes and the second half in twos. That is what the sources mean when they describe the soleá as a mixture of triple and duple bars, and it is why clapping it as two even bars of six loses the accents that make it itself.
The cadence
The soleá sits in the flamenco mode, and its source places it por arriba: the home chord’s root on the open sixth string, so the page opens in E. The cadence below the cycle is the four-chord fall its source prints for the soleá, landing on the home chord. Singers do not all sit in E, and guitarists move the capo to meet them; pick another key and the same four chords are realised there. The cycle does not move at all when the key does, which is the whole point of counting it separately.