The theory of the reactive collision of an atom with a diatomic molecu
le is formulated in ''democratic'' hyperspherical coordinates. An adia
batic ansatz is used to separate the distance coordinate from the angu
lar coordinates. The angular eigenvalue problem is solved, using the h
yperspherical harmonics as basis functions, while the R-matrix propaga
tion method is used to integrate the resulting coupled equations along
the distance coordinate. As an example, reactive collision probabilit
ies for H + H-2 are computed, using the Por-ter-Karplus surface. The s
ymmetry requirements, when dealing with three identical Fermions in th
e collision, are considered explicitly.