The Fang Regalia was known as the Bloody Armour Fang on Gigaers during the time it was owned by Udou Akira. The Fang Regalia is no longer the complete part it was when owned by Falko of the Original Sleeping Forest. Rather, the Fang Regalia is now comp
rised solely of the system responsible for the creation of the Fang through the collection of Inertial Energy that comes from landing and breaking and allows it to be remitted.
However, this system is a double-edged sword for the wielder of the Fang Regalia, for although it makes the production that creates Fangs far easier, the complex mechanism has to be fitted into the narrow wheel space of the AT, and with it inserted, other functions of the AT have to be forfeited. Namely, the AT's ability to jump.
This is why the Fang Regalia, and indeed the Bloody Road, is often synonymous with the "creatures of the land". For by wielding the Fang Regalia, the user forfeits the "wings" their AT grants them in order to achieve a stronger and more efficient Fang.
The name of the Fang Regalia's core is never mentioned so far in the manga, although some name appearances of the Fang Regalia is quite often. This however, not leave this regalia in total mystery. Names such as Bloody Armor - Fang on Gigaers, is the name of Udou Akira's activated Fang Regalia's AT. Also on Kogarasumaru vs. First Generation Sleeping Forest arc, Agito unleashes the true power of his regalia after him being tuned with Nakayama Yayoi, which tells Agito's AT name; Bloody Armor - Sand Tiger.
So, it is possible that the name of this regalia's core is Bloody Armor. Its Infinite Atmosphere trick is Infinity Jail.
The Fang Regalia originally belonged to Falco, but lost them during the fall of the first Sleeping Forest. They were given to other riders, eventually becoming Agito's, then Akira's, then back to Agito. After Nike was defeated by Kazu, ending the fight on Genesis's carrier, Agito gave the Fang Regalia's Core to Ikki.
Solid Fang - The creation of this Fang is through the collection of Inertial Energy that comes from landing and breaking and allows it to be remitted. However this Fang is more concentrated than normal and is able to actually cut things.
AGITO Bloody fang Ride fall "Leviathan" Akito's signature trick, it is the basic 'Fang' attack. Agito is able to perform it without Bloody Armor, a spectacular feat in and of itself.
Gigaers Cross - Originally Udō Akira's technique, Agito has also used it. It is a pair of fangs fired in a cross-shaped configuration.
Cage of Fangs - Originally Udō Akira's technique, Agito has also used it. As its name implies, it is a criss-crossing collection of Fangs which converge upon the opponent.
Bloody Fang: Infinity Jail - Lind's signature trick, it invokes the Infinity Atmosphere of the Bloody Road to create a ball of Fangs, resembling Agito's cage, that encloses the opponent. It is essentially a refined, more elegant version of the "Cage of Fangs", as the 'Jail' can be imploded at the user's will.