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Fibonacci (21,13) Hyper Knot V2 (218k) | PAPP

Sketchfab
3D Model

Fibonacci (21,13) Hyper Knot V2 (218k) | PAPP

Description

A (21,13) torus knot — where 21 and 13 are consecutive Fibonacci numbers F(8) and F(7). The ratio p/q = 1.61538... approximates the golden ratio φ with Δ = 0.0026, making this a topological embedding of φ convergence. Anatomy: 218,400 vertices, 420,000 faces, 638,400 edges. Built with exact Frenet-Serret frames (TNB orthogonality verified to 0.000000). The tube is a true polygon mesh, not wireframe — 8,400 core curve points × 24-sided cross-sections. Color = Geometry: Vertex color encodes local curvature κ (warm = high bending) and torsion τ (violet shift at twist peaks). Brightness tracks radial position on the torus. 48,000 unique colors, zero cosmetic. Inner Ribbon: A Seifert-inspired ribbon surface (16,800 faces) runs inside the tube, revealing the knot's twist structure and linking number = 273. Topology: 21 full azimuthal turns, 26 meridional crossings. Single connected solid. Generated via PAPP Framework.
Sketchfab
3D Model

Fibonacci (21,13) Hyper Knot V2 (218k) | PAPP

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Asset Information

Type:

3D Model

Source:

Sketchfab

Download:

Available

Published:

February 26, 2026

License:

CC Attribution

Commercial Use

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Statistics

Downloads:

1

Likes:

0

Views:

3

Technical Specifications

Polygons:

420,000

Vertices:

218,400

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