### Abstract

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.

Original language | English |
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Pages (from-to) | 845-851 |

Number of pages | 7 |

Journal | Proceedings of the American Mathematical Society |

Volume | 117 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1993 Mar |

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### Keywords

- Geometric structure
- Hyperbolic geometry
- Moduli space
- Similarity class

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics