dʒˈaɪɡæks mˌeɪd hɪz deɪbjˈuː fɚðə swˈɪs nˈæʃənəl tˈiːm ˌɔn θˈɜːɾi wˈʌn mˈɑːɹtʃ tˈuː θˈaʊzənd fˈoːɹ, ɹᵻplˈeɪsɪŋ hˈækən jˈækɪn ˈæftɚ sˈɪksti mˈɪnɪts əvə wˈʌn zˈiəɹoʊ fɹˈɛndli lˈɔs tə ɡɹˈiːs ɪn həɹˈækliən.
Gygax made his debut for the Swiss national team on 31 March 2004, replacing Hakan Yakin after 60 minutes of a 1–0 friendly loss to Greece in Heraklion.