The three have never interacted in canon due to being in different games, with Kokichi also being from a different saga. However, Nagito kidnapped and used Byakuya as a hostage in Danganronpa Another Episode: Ultra Despair Girls. Nagito and Kokichi also shared one event together in Ultimate Talent Development Plan, the non-canonical bonus mode of Danganronpa V3.
In certain ways, the three are polar opposites, with Byakuya being cold-hearted, distant, and being the only one out of all the Rivals not to obsess over one of the game's main themes (a trait instead given to Junko Enoshima); Nagito having an obsession with hope and caring more about his classmates than himself, and Kokichi being playful and manipulative. However, they all share their role as the Rival in their respective game, being the most antagonistic among the students, but not the masterminds.
Their another similarity is that they all have a soft spot for the protagonist of their respective game. Byakuya has many 'Pet the Dog' moments with Makoto Naegi and seems to respect him more than he does anyone else. Nagito has shown clear attraction towards Hajime Hinata and has a crush on him in his Free time Events and Island Mode. Meanwhile, Kokichi seems to trust Shuichi Saihara more than any of his other classmates and has shown attraction towards him in his Free Time Events and Island Mode as well.
They all are also characterized as being the ones who always tried to "ruin" the Class Trials for the others. Togami framed Genocide Jack for being Chihiro Fujisaki's killer just to make things more interesting for him and perform an experiment to see who he'd have to watch out for in case he decides to become the blackened. Komaeda was always the most suspected one in every trial because of his behavior towards the survivors and created a case where he sacrificed himself for the "traitor" to survive alone. Finally, Oma's case was similar to Nagito's, always being suspected and blamed, manipulating Gonta Gokuhara into killing Miu Iruma, and creating a seemingly unsolvable murder.
All three also use a sort of reverse psychology during the trials, putting the suspicion on someone's back, even though they know full well that this person isn't the culprit, just to have their name cleared in a roundabout way.
The ship sailed as a result of the three being the Rivals of their games and having many similar traits. However, this ship is often overshadowed by their much more popular ships with the protagonists (Naegami, Komahina, Oumasai). The ship can also being referred as the "gay for the protagonist" squad, with their main rivals being the protagonists' love interests.
The name for the ship came from the trio's antics during Class Trials. It is mostly used on forums, primarly Reddit. Interestingly, while it's partly fitting, considering the chaos all three of them cause, it's also partly misleading, considering the fact that their roundabout ways of clearing the others' names help to progress the debates and steer the survivors towards the right answer.
A different version of this polyship may also include the Rival from Future Arc of Danganronpa 3: The End of Hope's Peak Academy, Kyosuke Munakata. However, with Munakata being slightly older and Danganronpa 3 receiving mixed feedback, this version wins in popularity.
- Komagami refers to the ship just between Byakuya and Nagito.
- Oumaeda refers to the ship just between Kokichi and Nagito.
- Oumagami refers to the ship just between Byakuya and Kokichi.