Two-sided bounds for dihedral angle sums of path and 4-ball tetrahedra
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914251347591168 |
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| author | Korotov, Sergey Krizek, Michal |
| author_facet | Korotov, Sergey Krizek, Michal |
| contents | A tetrahedron is called a path tetrahedron, if it has three mutually orthogonal edges that do not intersect at a single point. A tetrahedron is called a 4-ball tetrahedron, if there exists a sphere tangent to all its edges. We derive two-sided tight bounds for dihedral angle sums of such tetrahedra. In particular, we prove that this sum lies in the interval (2π, 2.5π) for path tetrahedra and in [6 arccos 1/3, 3π) for 4-ball tetrahedra. Also some of their useful properties are presented. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_08304 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Two-sided bounds for dihedral angle sums of path and 4-ball tetrahedra Korotov, Sergey Krizek, Michal Metric Geometry 51M04, 51M20, 52A20, 65N30 A tetrahedron is called a path tetrahedron, if it has three mutually orthogonal edges that do not intersect at a single point. A tetrahedron is called a 4-ball tetrahedron, if there exists a sphere tangent to all its edges. We derive two-sided tight bounds for dihedral angle sums of such tetrahedra. In particular, we prove that this sum lies in the interval (2π, 2.5π) for path tetrahedra and in [6 arccos 1/3, 3π) for 4-ball tetrahedra. Also some of their useful properties are presented. |
| title | Two-sided bounds for dihedral angle sums of path and 4-ball tetrahedra |
| topic | Metric Geometry 51M04, 51M20, 52A20, 65N30 |
| url | https://arxiv.org/abs/2601.08304 |