Members of Faction Paradox sometimes wore full ceremonial armour, which included their skull masks.
Faction Paradox members wore their armour to diplomatic meetings and sometimes in battle. The classic, full armour appeared to be made from the bones of very tall, vampiric creatures, taken from an "abomination's graveyard" found by the Grandfather's four Godfather-lieutenants. The Faction claimed that they were the skeletons of Great House members from a timeline where they lost the war against the Yssgaroth and were overcome by the taint. This irritated the Houses not only because it was an emblem of their failure, but because the Houses insisted that alternative timelines did not exist at all.
The full armour was not actually worn by all Faction members. Most Cousins only possessed a ceremonial mask, and the Military Wing in the Eleven-Day Empire used simpler armour which left the face clear, apparently taken from smaller Yssgaroth-taint-bearers, possibly "second-generation Mal'akh". Even members with full-body armour sometimes used skulls that differed from the bat-like norm and seemed to be taken from "other species of giants altogether"; for example, Cousin Belial wore a tusked, mammoth-like headpiece, (PROSE: The Book of the War) and Cousin Shuncucker wore armour which she claimed came from a leviathan. (AUDIO: Movers) Godfather Avenir told Cococyte that the Faction wore "the skulls of the creatures that never have been", and temporarily adopted a simple human skull as a mask to demonstrate to Cococyte "how serious things [had] become" when Cococyte's abuse of the Observer Effect temporarily threatened to erase the whole existence of humanity. (PROSE: Marticide)