Geodesic
A New Classification of Convex Tetragons
Journal for geometry and graphics, Tome 26 (2022) no. 2, pp. 271-288.

Voir la notice de l'article provenant de la source Heldermann Verlag

This work is a continuation and expansion of a previous work of the author [Math. Gazette 106/566 (2022) 269--280]. In this respect a diagram is constructed with sixty-five different economical definitions of thirty-five families of convex tetragons defined hierarchically on the basis of equal sides, equal angles, and equal diagonal segments. The diagram allows us to appreciate the existing duality between the definitions that include equality of sides and angles, among those that include equality of sides and diagonal segments, as well as those that include equality of angles and diagonal segments. It will also be possible to appreciate the existing duality between the definitions that include equality of sides and angles with the definitions that include equality of sides and diagonal segments. As an extension of the paper cited above we analyze which families are defined and the economic hierarchical definitions for these families when the tetragon has perpendicular diagonals. A diagram of these last families is constructed.
Classification : 51M04
Mots-clés : Tetragon definition, convex tetragon classification 
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M. Dalcín . A New Classification of Convex Tetragons. Journal for geometry and graphics, Tome 26 (2022) no. 2, pp. 271-288. http://geodesic.mathdoc.fr/item/JGG_2022_26_2_JGG_2022_26_2_a5/