The Wire Polyhedron Mode: The Edge Threshold Shrinks as You Add Nodes

Wire Polyhedron is the Lattice engine at its most three-dimensional: a rotating wireframe solid whose vertices ride their own bands. It is not a fixed solid with a fixed number of faces. It is a point cloud on a sphere, plus a rule about which points count as neighbours, and the rule is the interesting part.

Vertices from the golden angle

Points are placed with the Fibonacci sphere construction: walk the vertical axis in even steps, and at each step rotate by the golden angle, which is pi times three minus the square root of five. The result is an even spread over the whole sphere with no poles, no seams and no clustering, for any count at all, computed in one pass with no relaxation step.

This is why the mode covers a tetrahedron and a geodesic dome with the same code path. A face list would have to be authored per solid. A spacing rule does not care.

The threshold that shrinks

An edge is drawn between two vertices when the straight-line distance between them on the unit sphere is under a threshold. That threshold is 2.2 divided by the square root of the node count.

The square root is doing real work. Spread N points evenly over a sphere and the typical distance to a neighbour falls roughly as one over the square root of N, because you are packing N points into a fixed area. So a FIXED threshold would connect each point to more and more neighbours as the count rose, and past a certain density every point would reach every other: the shell would become a solid ball of lines. Dividing by the square root keeps the number of neighbours per vertex roughly constant, so raising the count gives you a finer mesh rather than a darker blob.

Depth without a depth buffer

There is no z-buffer here, and none is needed. An edge's opacity is built from two things: how short it is relative to the threshold, so borderline edges fade in rather than popping, and the average depth of its two endpoints, so edges on the far side of the sphere are drawn dimmer than edges on the near side. That is enough for the eye to resolve which surface is in front. Vertical positions are also squashed to 94% of horizontal, which is a small cheat that reads as perspective.

The solid turns on two axes at different rates, one of them offset by the Twist control, so it never settles into a single obvious spin. Rotation ships at 0.18 and scales both.

Every vertex rides its own band

Each node is stamped at a size built from its own slice of the spectrum plus the beat pulse, then scaled by its depth. So a loud frequency does not brighten the whole solid, it swells the particular vertices that own it, and the shape visibly deforms in one region rather than pulsing as a unit. Geometry is scoped to this mode alone in the engine, because it is the only Lattice mode that stamps points rather than stroking or filling cells, so the vertices can be squares, stars or soft glows.

The overall radius rises with the routed level and the beat, soft-limited to 94% of the contain radius so the solid can breathe without touching the frame edge. Audio contribution IS in scope for this mode, and the level it produces is what that radius reads.

When to reach for it

Electronic, progressive, technical metal, science and technology content, and any brief that asks for something that looks engineered. It is the only mode in this wave from an engine that had no mode article at all, and the engine's own guide is the place to see what sits beside it: The Lattice Engine.

Open Wire Polyhedron in the gallery or go to the editor.