Some Questions about Regular Maps

As you learn about regular maps, you may wonder whether a regular map can have some property; and if it can, what is the smallest such map. This page lists some such questions, with their answers.

The word "smallest", used here, may be taken to mean "having the fewest edges", or alternatively, as "in the surface of lowest genus".

• What is the smallest chiral regular map? answer
• What is the smallest chiral regular map in a higher genus than that of the answer above? answer
• What is the smallest non-orientable chiral regular map? answer
• What is the smallest pair of regular maps in the same genus and having the same Schläfli symbol and the same number of edges? answer
• What is the smallest regular map with a Schläfli symbol of the form {p,p} but not self-dual? answer

Index to Regular Maps
Glossary for Regular Maps