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PreprintarXiv licencearXiv

The Exact Dihedral Angle Sum Range for Circumcentral-Cevian Jaw Tetrahedra

  • Sergey Korotov
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Abstract

Hajja, Hammoudeh, Hayajneh and Martini showed that a tetrahedron whose cevians to the circumcenters of the opposite faces are concurrent is either a kite or a special jaw. We determine the exact dihedral-angle-sum range on the jaw component. The lower endpoint is attained only by the regular tetrahedron, while the upper endpoint is approached only in the degenerate limit. The proof reduces the family to one scale-invariant parameter and an explicit monotonicity argument.

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Cite

BibTeXRIS
BibTeX
@misc{korotov2026exact,
  title = {{The Exact Dihedral Angle Sum Range for Circumcentral-Cevian Jaw Tetrahedra}},
  author = {Sergey Korotov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33783},
  eprint = {2610.33783},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33783},
}
RIS
TY  - UNPB
TI  - The Exact Dihedral Angle Sum Range for Circumcentral-Cevian Jaw Tetrahedra
AU  - Sergey Korotov
PY  - 2026
DA  - 2026/10/24
PB  - arXiv
DO  - 10.48550/arxiv.2610.33783
UR  - https://arxiv.org/abs/2610.33783
AB  - Hajja, Hammoudeh, Hayajneh and Martini showed that a tetrahedron whose cevians to the circumcenters of the opposite faces are concurrent is either a kite or a special jaw. We determine the exact dihedral-angle-sum range on the jaw component. The lower endpoint is attained only by the regular tetrahedron, while the upper endpoint is approached only in the degenerate limit. The proof reduces the family to one scale-invariant parameter and an explicit monotonicity argument.
ER  -