Impurity of the corner angles in certain special families of simplices

DOI10.1007/s00022-014-0219-1zbMath1309.51012OpenAlexW2132106079MaRDI QIDQ2255395

Mowaffaq Hajja, Mostafa Hayajneh

Publication date: 9 February 2015

Published in: Journal of Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00022-014-0219-1

zbMATH Keywords

quadratic formcorner angleCayley-Menger determinantorthocentric simplexcircumscriptible simplexisodynamic simplexisogonic simplextetra-isogonic simplexCayley-Menger matrixpure polyhedral angle

Mathematics Subject Classification ID

(n)-dimensional polytopes (52B11) Special polytopes (linear programming, centrally symmetric, etc.) (52B12) Three-dimensional polytopes (52B10) Polyhedra and polytopes; regular figures, division of spaces (51M20) Length, area and volume in real or complex geometry (51M25) Symmetry properties of polytopes (52B15)

Related Items (4)

Irreducibility of the Cayley-Menger determinant and of a class of related polynomials ⋮ Pre-kites: simplices having a regular facet ⋮ The sum of measures of the angles of a simplex ⋮ Pompeiu-like theorems for the medians of a simplex

Cites Work

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• Orthocentric simplices as the true generalizations of triangles
• The open mouth theorem in higher dimensions
• The sum of measures of the angles of a simplex
• The pons asinorum and related theorems for tetrahedra
• Coincidences of centers of edge-incentric, or balloon, simplices
• The Pons asinorum for tetrahedra
• The law of sines for tetrahedra and \(n\)-simplices
• The open mouth theorem, or the scissors lemma, for orthocentric tetrahedra
• Orthocentric simplices and their centers
• More characterizations of certain special families of simplices
• Pythagoras' Theorem for Areas
• The Pons Asinorum in higher dimensions
• Then-dimensional pythagorean theorem
• The n-Dimensional Pythagorean Theorem via the Divergence Theorem
• The Circumradius of a Simplex
• Letter to the editor

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