A geometrical one-to-one correspondence is given between partitions of a rooted polygon into pentagons and a family of rooted planar maps, called planar maps of order one (each edge having at least one extremity incident to the exterior face), with a bridge root edge.
@article{hal-00021844,
author = {Micheli, Anne and Arqu\`es, Didier},
title = {Pentagon partitions of polygons and a special class of planar maps},
journal = {HAL},
volume = {2001},
number = {0},
year = {2001},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00021844}
}
Micheli, Anne; Arquès, Didier. Pentagon partitions of polygons and a special class of planar maps. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-00021844/