2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159493We consider an SO(4) Euler rigid body with two 'inertia momenta' coinciding. We study it from the point of view of bihamiltonian geometry. We show how to algebraically integrate it by means of the method of separation of variables.This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/Mathematical PhysicsDifferential GeometryExactly Solvable and Integrable Systems37K10; 70H20; 14H70text