[en] Properties of acceptance and beam transmission in a triangle design of the neutrino factory muon decay ring, with decay straights based on solenoidal focusing, are reported.The muon storage ring in the neutrino factory, NuFact, is located at the high energy end of the muon acceleration chain. It delivers the μ⁺/μ^- decay neutrinos to physics detectors. The design of concern here, is a triangle geometry 20 GeV storage ring, upgradable to 50 GeV, (the parameters are given), which features two decay straight sections, each one aiming at a distant detector. The third straight section of the ring is devoted to tuning, collimation and RF. A particularity of the proposed design, is in its being based on solenoid focusing decay straights, which has the virtue of minimizing the betatron amplitudes, compared to equivalent quadrupole focusing. The solenoidal focusing ensures the requested ratio, for the r.m.s. divergences of the 20 GeV muon and the neutrino beam, of 0.1 for an assumed muon normalized r.m.s. emittance of 4800 π mm mr (3 π cm, total). The goal of the present work is to show the viability of this design, in particular as concerns the impact of the solenoid focusing on machine behavior. It addresses the questions of residual coupling, machine acceptance, and concludes with a computation of beam transmission over 1000 turns. The paper has the following structure: 1. Introduction; 2. Working hypothesis; 3. Building-up ray-tracing data; 3.1. Arcs; 3.2. Solenoid straight; 3.3. Tuning/Collimation/RF straight; 3.4. Full ring; 3.4.1. Beam envelopes; 3.4.2. Closed orbits; 3.4.3. Momentum dispersion; 3.5 Large amplitude tracking, preliminary tests; 4. Tracking, linear machine; 4.1. Large amplitude tracking; 4.1.1. 2-D horizontal initial conditions; 4.1.2. 2-D vertical initial conditions; 4.1.3. 4-D + δp/p initial conditions; 4.2. Transmission, 4-D + δp/p, no sextupoles; 4.2.1. ε_x ε_z = 3 π cm (norm.), δp/p = ±1%; 4.2.2. ε_x ε_z = 6 π cm (norm.), δp/p ±4%; 5 Transmission, 4-D + δp/p, chromaticity corrected; 5.1. Chromaticity correction; 5.2 Transmission; 6. Conclusion; Appendix: Closed orbit induced by chromaticity sextupoles. In conclusion one stresses that this tracking study shows that the principle of a triangle muon storage ring based on solenoidal focusing, and with apex angle consistent with two baselines, fulfills acceptance requirements. Detailed investigations need be pursued, though, for instance on principle chromaticity corrections