Geigi is a progressive man, possibly as progressive, in his way, as his aiji Tabini is. He welcomes new technology and was appointed the atevi lord in charge on the space station. He is described as good-humored and congenial, and rotund in appearance. He is styled as Lord Geigi of Kajiminda, Lord of Sarini Province, third holder of the Treaty of Aregorji, Viceroy of the Heavens and Stationmaster of Alpha Station. As of the end of Deceiver, he is also clan head of the Maschi. As of the end of Betrayer, he has passed the position of clan head to a member of a sub-clan of Maschi.

Geigi is Maschi, a clan which is dying out. His parents were Seigen of the Maschi and Tosi of the Sulesi. His last contracted wife was of sub-clan Paru of Samiusi clan; Paru has an affiliation with Hagrani clan of the Taisigi. Her sister married into the Marid. He himself has had at least one Marid wife. However, none of his contracts have produced heirs. His sister is Tejo, who has a son Baiji by her husband Dumaei. Dumaei's clan is not named. Both Tejo and Baiji are Maschi.

Geigi's west coast estate is Kajiminda, on Kajidami Bay on the southwestern coast, in Sarini province. The next estate north of his and on the Najida peninsula between Kajidami Bay and Najidami Bay is Najida, Bren Cameron's estate. The township south of Kajiminda is Dalaigi. Dalaigi is the largest town on the western coast, has a large airport and is a major transport hub for the region. Separti township also lies in that direction and shares the airport; it is inland of Dalaigi. North of the peninsula is Mogari-Nai. West is Mospheira. East is the main Maschi estate at Targai, and the continental interior.

Geigi has two major-domos, both mentioned in Deceiver. They are Peisi, who is Edi and major-domo of Kajiminda, and Barati, who is his major-domo on the space station.

His senior bodyguards as of Deceiver are Haiji and Cajami; his junior bodyguards are Saoji and Sakeimi.

Both Kajiminda and Najida are served by people who are mostly Edi. Aboriginal to Mospheira, they were resettled to the western coast when the island was ceded to humans. This diminished the power of the Marid, which held the area before; they want it back.