In this paper we construct a natural geometric structure for the space of shapesof a star-shaped polygon. Roughly speaking we find: The set ofsimilarity classes of marked stars forms a hyperbolic right angle pentagon bundle over the space of external angle sets ofinscribed pentagons.The assignment of the shape of its fiber to each angle setforms a hyperbolic plane bundle over the Teichmiiller space of hyperbolic right angle pentagons. Any automorphism induced by renumbering is compatible with these geometric structures.
ASJC Scopus subject areas
- Applied Mathematics