Constraint-guided equal-strut growth generates a tunable family of DNA-realizable wireframe filaments

Wireframe DNA nanostructures are built from edges of prescribed length meeting at vertices of prescribed valency, which makes their design space a geometric one: which equal-edge frameworks can be built at all, given a maximum vertex degree, a minimum edge angle and a steric clearance. We apply a constrained growth construction—each new vertex placed by trilateration at a fixed strut length from at least three placed vertices, accepted only if the resulting framework still satisfies the design constraints—and report three results. First, under a degree cap of six the construction is extremely selective: of all periodic face-choice patterns tested, only the Boerdijk–Coxeter tetrahelix grows without stalling, and it does so because its interior vertices have degree exactly six, saturating the budget. Second, raising the cap to seven unlocks a one-parameter family of kinked variants indexed by the defect spacing k, whose radius is programmable from 0.52 to 1.13 strut lengths and whose handedness alternates with k, while straightness stays above 0.99. Values k ∈ {3, 5, 8} stall for an identifiable reason—the capped vertex lands at unit distance from a fourth earlier vertex—and run freely at a cap of eight. Both caps are within demonstrated multi-arm junction capability. Third, two members of the family, the pure tetrahelix and a k = 6 variant, were routed into DNA, energy-minimised and run for 5×105 oxDNA steps at 30◦C: both are stable, with second-half mean energies −1.4919±0.0017 and −1.5004 ± 0.0019 per nucleotide and shape changes under 4%. The kinked variant routes into 8 strand cycles against the tetrahelix’s 22. We also report what did not survive checking: a twist–stretch coupling that vanished under length convergence, and a circular-dichroism sign rule that its own descriptor failed to predict.