Angles — are you talking geometry here?
The 9 Choirs of Angels
In ascending order:
Angels
Archangels
Principalities
Powers
Virtues
Dominations
Thrones
Cherubim
Seraphim
Note:
The Choir of Angels is divided into three triads with specific concerns:
The 1st triad:
Angels, Archangels, and Principalities: concern themselves with the minute ordering of the universe and specific causes, including the welfare of people. Each human being, each church, and each country has a Guardian Angel. The Feast of the Guardian Angels is October 2.
The 2nd triad:
Powers, Virtues and Dominations: known as the “angels of creation” because they concern themselves with the ordering of the universe and a plurality of causes.
The 3rd triad:
Thrones, Cherubim, and Seraphim: concern themselves with contemplating the glory of God. It is the 6-winged Seraphim who sing the Sanctus, “Holy, Holy, Holy Lord God of Hosts” (Isaias 6:3).