The 4-D Hyper-Triskelion: A New Parametric Embedding of the Ancient Triskelion Symbol in Four Dimensions
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| Natura: | Recurso digital |
| Lingua: | inglese |
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Zenodo
2025
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| _version_ | 1866901851722481664 |
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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 |