The 4-D Hyper-Triskelion: A New Parametric Embedding of the Ancient Triskelion Symbol in Four Dimensions

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Autore principale: Stone, Shane Edward
Natura: Recurso digital
Lingua:inglese
Pubblicazione: Zenodo 2025
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author Stone, Shane Edward
author_facet Stone, Shane Edward
contents <p>Abstract </p> <p>This work introduces the 4-D Hyper-Triskelion, a new mathematical surface defined by a two-parameter embedding of the ancient three-armed triskelion motif into four-dimensional Euclidean space. While triskelion patterns appear throughout ancient cultures—Celtic spirals, Greek triple curves, and megalithic carvings—these representations have historically been restricted to 2-D symbols or 3-D artistic interpretations.</p> <p>Here we present, for the first time, a rigorous 4-D parametric generalization using angular coordinates (φ, θ) with a tri-lobe modulation encoded in the mode 3φ. This embedding produces a smooth toroidal-like manifold whose cross-section executes a threefold rotational symmetry within an orthogonal plane.</p> <p>The 4-D Hyper-Triskelion extends the classical torus, preserves the triskelion’s characteristic triplet structure, and establishes a foundation for applications in higher-dimensional visualization, topology, symbolic geometry, computational modeling, and mathematical aesthetics.</p> <p>License: CC-BY-4.0<br>Authors: Shane Edward Stone </p> <p>Simulations conducted by AI collaborator Kaelen</p> <p> </p> <p>Extended  Fourth Dimensional Parametric Family of the Hyper-Triskelion can be found here. https://zenodo.org/records/17624358</p> <p> </p>
format Recurso digital
id zenodo_https___doi_org_10_5281_zenodo_17919636
institution Zenodo
language eng
publishDate 2025
publisher Zenodo
record_format zenodo
spellingShingle The 4-D Hyper-Triskelion: A New Parametric Embedding of the Ancient Triskelion Symbol in Four Dimensions
Stone, Shane Edward
Four Dimensional Objects
Parametric Objects
Mathematics
Mathematical analysis
Mathematical model
Software
Mathematics
Geometry
<p>Abstract </p> <p>This work introduces the 4-D Hyper-Triskelion, a new mathematical surface defined by a two-parameter embedding of the ancient three-armed triskelion motif into four-dimensional Euclidean space. While triskelion patterns appear throughout ancient cultures—Celtic spirals, Greek triple curves, and megalithic carvings—these representations have historically been restricted to 2-D symbols or 3-D artistic interpretations.</p> <p>Here we present, for the first time, a rigorous 4-D parametric generalization using angular coordinates (φ, θ) with a tri-lobe modulation encoded in the mode 3φ. This embedding produces a smooth toroidal-like manifold whose cross-section executes a threefold rotational symmetry within an orthogonal plane.</p> <p>The 4-D Hyper-Triskelion extends the classical torus, preserves the triskelion’s characteristic triplet structure, and establishes a foundation for applications in higher-dimensional visualization, topology, symbolic geometry, computational modeling, and mathematical aesthetics.</p> <p>License: CC-BY-4.0<br>Authors: Shane Edward Stone </p> <p>Simulations conducted by AI collaborator Kaelen</p> <p> </p> <p>Extended  Fourth Dimensional Parametric Family of the Hyper-Triskelion can be found here. https://zenodo.org/records/17624358</p> <p> </p>
title The 4-D Hyper-Triskelion: A New Parametric Embedding of the Ancient Triskelion Symbol in Four Dimensions
topic Four Dimensional Objects
Parametric Objects
Mathematics
Mathematical analysis
Mathematical model
Software
Mathematics
Geometry
url https://doi.org/10.5281/zenodo.17919636