Abstract

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Symmetry: Culture and Science
Volume 35, Number 3, pages 351-354 (2024)
https://doi.org/10.26830/symmetry_2024_3_351

THE HYPER-EUCLIDEAN GEOMETRY HENRI POINCARÉ REQUESTED

Renate C.-Z.-Quehenberger

The Institute for a Global Sustainable Information Society, Vienna, Austria.
Email: renate.quehenberger@gsis.at

Abstract: Poincaré introduced the fundamental group in terms of closed paths in a manifold and is building on his experience with Fuchsian groups where each group is associated with a fundamental polygon on the hyperbolic plane with edges identified by certain motions. Let us recall Poincaré’s two questions: 1) Given a schema, does there always exist a corresponding polyhedron? and 2) If two polyhedra have the same schema, are they homeomorphic?In this context we suggest examining the heptahedra pair E±. In any case they satisfy Poincaré’s definition by being bounded by hyperplanes

Keywords: Translational symmetry, audiolexeme, videolexeme

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