Abstract
In this paper, the families of orthocentric, circumscriptible, isodynamic, and isogonic (or rather, tetra-isogonic) \(d\)-simplices, \(d \ge 3\), are considered, and it is proved that the intersection of any two of them is precisely the family of \(d\)-kites. Here, a \(d\)-simplex is called a \(d\)-kite if \(d\) of its vertices form a regular \((d-1)\)-simplex whose vertices are equidistant from the remaining vertex.
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Hajja, M., Hammoudeh, I. & Hayajneh, M. Kites as the only doubly special simplices. Beitr Algebra Geom 56, 269–277 (2015). https://doi.org/10.1007/s13366-014-0204-8
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DOI: https://doi.org/10.1007/s13366-014-0204-8
Keywords
- Circumscriptible simplex
- Isodynamic simplex
- Isogonic simplex
- Kite
- Orthocentric simplex
- Quadratic form
- Special simplex
- Tetra-isogonic simplex