Polarity for a simplex

Sahib Ram Mandan

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Dandelin’s figure in $n$ -space

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Gergonne and Nagel points for simplices in the $n$ -dimensional space.

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Self-similar simplices.

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A note on intersections of simplices

David A. Edwards, Ondřej F. K. Kalenda, Jiří Spurný (2011)

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We provide a corrected proof of [1, Théorème 9] stating that any metrizable infinite-dimensional simplex is affinely homeomorphic to the intersection of a decreasing sequence of Bauer simplices.

Combinatorial lemmas for polyhedrons I

Adam Idzik, Konstanty Junosza-Szaniawski (2006)

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We formulate general boundary conditions for a labelling of vertices of a triangulation of a polyhedron by vectors to assure the existence of a balanced simplex. The condition is not for each vertex separately, but for a set of vertices of each boundary simplex. This allows us to formulate a theorem, which is more general than the Sperner lemma and theorems of Shapley; Idzik and Junosza-Szaniawski; van der Laan, Talman and Yang. A generalization of the Poincaré-Miranda theorem is also...