Ibitani clearly admires Machimiya a great deal. He is even visibly upset when thinking about how Machimiya broke up with his girlfriend in order to prepare for the Inter High. Machimiya, in turn, relies on Ibitani to help carry out his plan.
According to Ibitani, Machimiya broke up with his former girlfriend Kana in order to focus on training for the Inter High.
Although Machimiya initially detests Arakita for being part of Hakone Academy, taunting and violently headbutting him during their battle at the Inter High to the point of drawing blood, Arakita says that he doesn't hate Machimiya's type and that Machimiya resembles his past self. This prompts him to tell the story of when he first began cycling and how he learned to move forward. Arakita wins their battle and offers to buy Machimiya a Bepsi after the race. Machimiya accepts his loss to Arakita with surprising grace considering how hard and dirty he fought, and looks forward to that Bepsi, coming to admire Arakita and his cycling. By the time Arakita actually buys him Bepsi after the Kumamoto Race, it fizzes all over Machimiya's face. In the 3DS game, Machimiya follows Arakita to Hakone Academy's training camp with Sohoku in order to race Arakita again and repay him for that Bepsi. Watanabe has said that Machimiya attends Yonan University with Arakita and Kinjou after graduating high school.
On the first day of the Inter High, Machimiya is able to strike a deal with Midousuji that Kyoto Fushimi can pass Hiroshima, provided that they work together to defeat Hakone Academy on Day 3. However, when Hiroshima fails to produce results, Midousuji isn't bothered, as he has no use for them in the final stage of the race.