The atomic surfaces modelling technique has been used to solve the structure of the basic Ni-rich Al–Co–Ni decagonal phase. Formula Al_70.6Co_6.7Ni_22.7, space group P\overline{10}, five-dimensional unit-cell parameters: d ₁ = d ₄ = 4.752 (3) Å, d ₂ = d ₃ = 3.360 (2) Å, d ₅ = 8.1710 (2) Å; α₁₂ = α₃₄ = 69.295°, α₁₃ = α₂₄ = 45°, α₁₄ = 41.410°, α₂₃ = α _i5 = 90° (i = 1–4), V = 291.2 (7) Å⁵; D_x = 3.887 Mg m⁻³. Refinement based on |F|; 2767 unique reflections (|F| > 0), 749 parameters, R = 0.17, wR = 0.06. Describing the structure of quasicrystals embedded in n-dimensional superspace in principle takes advantage of n-dimensional periodicity to select the minimal set of degrees of freedom for the structure. The method of modelling of the atomic surfaces yielded the first fully detailed structure solution of this phase. Comparison with numerous former, less accurate models confirms several features already derived, but adds a new essential insight of the structure and its complexity. The atoms fill the space forming recurrent structure motifs, which we will (generically) refer to as clusters. However, no unique cluster exists, although differences are small. Each cluster shows a high degree of structural disorder. This gives rise to a large configurational entropy, as much as expected in a phase which is stable at high temperature. On the other side, the cluster spatial arrangement is perfectly quasiperiodic. These considerations, corroborated by analysis of the structural relationship with neighbouring periodic phases, strongly suggest the existence of a non-local, long-range interaction term in the total energy which may be essential to the stability.