The three have only had one interaction in the canon, which is when Rantaro says he will end the game of death, to which Korekiyo asks him how he intends to do it. Angie says she will pray for Rantaro's success, but that if he was lying she would punish him, which Rantaro interprets as a threat, but remains calm about it. At first Korekiyo suspects that he just said that to calm Ryoma down, but Angie tells him that there's no way he could have known that.
Korekiyo showed great admiration for both Angie and Rantaro, but this is due to the fact that he admires humanity in general. Rantaro and Angie there are not many interactions in canon and there are no interactions UTDP, but Korekiyo has interactions with both. In Korekiyo and Rantaro's they talk about their travels and their sisters, while in Korekiyo's with Angie, Korekiyo commented on his interests in acting from a Christian point of view, which made Angie a little angry and said he would have pray not to face The judgement.
The three have opposite personalities, although they are seen as mysterious individuals, Rantaro seems to be more calm and carefree, Korekiyo is considered somewhat disturbing and cool-headed, while Angie is positive and cheerful. Despite the differences, Korekiyo shares common interests with both, Angie on areas of culture, art and religion, and Rantaro on world travel and the relationship between her sisters.
Because Amaguji and Shinnaga are the most popular ships for Korekiyo, the poly has gained many shippers, they like the dynamic between a calm person, a serious and an agitated. Still, it's still a rare pair in fandom, having only three stories on AO3 and nine posts on tumblr. Despite this, most prefer Korekiyo's solo ships with Rantaro or Angie, and the poly ship is overshadowed by more popular ones like Amashinsai.
- Amaguji refers to the ship just between Rantaro and Korekiyo
- Amanaga refers to the ship just between Rantaro and Angie
- Shinnaga refers to the ship just between Korekiyo and Angie