Some recent papers on Platonic surfaces, more commonly known as regular maps
Surfaces having no regular hypermaps by Steve Wilson and Antonio Breda d'Azevedo, Discrete Math. 277 (2004), no. 1-3, 241--274.

Classification of regular maps of negative prime Euler characteristic by Antonio Breda d'Azevedo, Roman Nedela and Jozef Sirán, Trans. Amer. Math. Soc. 357 (2005), no. 10, 4175--4190 (electronic).

AMS review of Platonic hypermaps by Antonio J. Breda d’Azevedo and Gareth A. Jones, Beitrage Algebra Geom. 42 (2001), no. 1, 1-37.

AMS review of Chiral hypermaps of small genus by Antonio J. Breda d’Azevedo and Roman Nedela, Beiträge Algebra Geom. 44 (2003), no. 1, 127--143. .

Determination of all regular maps of small genus. by Marston Conder and Peter Dobcsányi, J. Combin. Theory Ser. B 81 (2001), no. 2, 224--242. .

AMS review of Rotary hypermaps of genus 2 by by Antonio J. Breda d’Azevedo and Gareth A. Jones, Beiträge Algebra Geom. 42 (2001), no. 1, 39--58. .


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