What does this research mean for the field?

The normalized compact constant γ=343/3π≈0.902 uniquely characterizes the regular tetrahedron as a convex polyhedron based on its intrinsic geometric properties. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.ESTABLISHES_NEW_DIRECTION.

What question did this study set out to answer?

The aim is to create a unique representation of the regular tetrahedron using intrinsic geometric properties.

February 26, 2026Open Access

The Simplest Invariant Representation of the Regular Tetrahedron

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The aim is to create a unique representation of the regular tetrahedron using intrinsic geometric properties.
Constructed a constant γ by integrating geometric and group-theoretic properties.
Used geometric mean for unbiased aggregation of intrinsic values.
Derived relationships involving circumradius and inradius ratios.
Derived a compact constant γ=343/3π≈0.902 for the regular tetrahedron.
Proved a theorem linking vertex number and circumradius-inradius ratio to regular tetrahedron classification.
Introduced methods applicable to other Platonic solids, like the cube.

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Implication

Constructs a new representation of the regular tetrahedron, indicating a novel method for geometric identification.

Cite This Study

Jian Wen (2026) studied this question.

synapsesocial.com/papers/699fe35995ddcd3a253e718e https://doi.org/10.5281/zenodo.18753496

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The Simplest Invariant Representation of the Regular Tetrahedron

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Discussion

Implication

Cite This Study

The Simplest Invariant Representation of the Regular Tetrahedron

Key Points

Discussion

Implication

Cite This Study

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