Exploded torus

The ring is cut into 2P tube segments — alternating long and short — with a small gap of gap degrees between them, so the implied circle survives the explosion.

lenShort = (2π − 2P · gap · π/180) / (P(1 + lengthRatio))
lenLong = lengthRatio · lenShort

Both lengths come from the same budget: P long plus P short arcs and 2P gaps must add up to the full turn, which is what fixes lenShort.

Each segment is a capped tube: the cross-section disc is closed with an NV-gon fan at both ends and the cap normal follows the local tangent, so the pieces read as solid separated chunks rather than an open shell. Every segment is also nudged outward from the centre along its mid-angle direction by spread · r, which opens the ring up without breaking the rhythm.