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Tresses of polygons

Łupiński A., Petelczyc K., Prażmowski K.

Demonstratio Mathematica

2007

Vol. 40, nr 2

419-439

A class of configurations which can be considered as series of suitably inscribed closed polygons is introduced and some fundamental properties of them are established.

On set-theoretic and cyclic representation of the structure of barycentres

Łapiński M., Prażmowski K.

Demonstratio Mathematica

2004

Vol. 37, nr 3

619--638

In the paper certain abstract combinatorial structures are studied as representations of the structure of barycentres of all the subsimplices of a given simplex in an arbitrary Desarguesian affine space. General properties of the configuration of barycentres are characterized in terms of those combinatorial structures. Most essential parameters of these structures are established and relevant automorphism groups are characterized.