  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 $p\gamma$ 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.
