Kyprios is out of Polished Gem (Danehill), a winner at two who was fourth in the Gr.3 Athasi Stakes and twice Broodmare of the Year in Ireland, and is the latest of her 10 foals, all of them winners; eight are stakes winners. He is a full brother to Search For A Song, a dual winner of the Gr.1 Irish St Leger, the Group winner Falcon Eight, who won the Gr.3 Loughbrown Stakes, and the stakes winner Amma Grace, winner of the Listed Trigo Stakes. He is a half-brother to Free Eagle (High Chaparral), winner of the Gr.1 Prince of Wales's S. and a sire, Sapphire (Medicean), winner of the British Champions Fillies & Mares S., then a Group 2, the multiple Group winner Custom Cut (Notnowcato), who won three Group 2 races, and Valac (Dark Angel), a Group 3 winner in Australia. Polished Gem is a full sister to Dress To Thrill, winner of the Grade 1 Matriarch S. and grandam of Solene Lilyette, a Listed winner in Ireland.

Second dam Trusted Partner (Affirmed) won the Gr.1 Irish 1000 Guineas in 1988 and is the third dam of Leovanni (Kodi Bear), winner of the Gr.2 Queen Mary S. in 2024. She is also the ancestress of the sire Vert De Grece, winner of the Gr.1 Criterium International.

Third dam Talking Picture (Speak John) was a champion in the US and won the Grade 1 Matron S. and the Grade 1 Spinaway S. She has 11 winners, among them three more stakes winners by Affirmed: Easy To Copy, a Group 2 winner in Italy and the dam of the sire Two-Twenty-Two, a triple Group 3 winner; Low Key Affair, a Grade 3 winner in the US and third in the Gr.1 Moyglare Stud Stakes; and the Listed winner Epicure's Garden. Talking Picture is the ancestress of Gallante (Montjeu), winner of the Gr.1 Grand Prix de Paris and the Gr.1 Sydney Cup.

Polished Gem's descendants also include Thunder Moon (Zoffany), winner of the Gr.1 Vincent O'Brien National S. and a sire. Sapphire is the dam of Kiss For A Jewel, third in the Gr.2 Kilboy Estate Stakes, and Federica Sophia, second in the Gr.3 Stanerra Stakes. Epicure's Garden is the dam of the Group 2 winner Lisieux Rose and the grandam of Forgotten Rules, winner of the Gr.2 British Champions Long Distance Cup and third in the Gr.1 Gold Cup.