In this paper, we propose a hexagonal description for the flavor composition of ultrahigh-energy (UHE) neutrinos and antineutrinos, which will hopefully be determined at the future large neutrino telescopes. With such a geometrical description, we are able to clearly separate the individual flavor composition of neutrinos from that of antineutrinos in one single regular hexagon, which can be regarded as a natural generalization of the widely-used ternary plot. For illustration, we consider the $pp$ or $pgamma$ collisions as the dominant production mechanism for UHE neutrinos and antineutrinos in the cosmic accelerator, and investigate how neutrino oscillations in the standard picture and in the presence of Lindblad decoherence could change the flavor composition of neutrinos and antineutrinos at neutrino telescopes.
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