Sketchfab
3D Model
Fibonacci (21,13) Hyper Knot V2 (218k) | PAPP
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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
Author:
consciousfractalProfile:
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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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