While the 27-nakṣatra division is sidereal-stellar, the 12-rāśi division is ecliptic-solar — it slices the 360° ecliptic into twelve 30° segments. Each rāśi has a single graha-lord (with Rāhu and Ketu excluded from sign-lordship in the classical scheme). The lordship pattern is symmetric: the two luminaries (Sun and Moon) rule one sign each, while each of the other five grahas rules a contiguous pair.
BPHS Chapter 4 (Rāśi-svarūpa) gives the form and element of each sign. The four elements (tattvas) cluster: Aries-Leo-Sagittarius are agni-tattva (fire); Taurus-Virgo-Capricorn are pṛthvī (earth); Gemini-Libra-Aquarius are vāyu (air); Cancer-Scorpio-Pisces are jala (water). The mobility tri-division — cara, sthira, dvi-svabhāva — captures how strongly the sign's quality manifests.
Exaltation degrees are critical because they let you measure a graha's strength positionally. A graha in its uccha-rāśi at the exact uccha-degree has maximum sthāna-bala; the same graha 180° away is nīca and weakest. Phaladīpikā Ch. 2 lists all nine grahas' exaltation degrees.