Operations on maps

A decorated r, q) is a map obtained by adding some vertices and edges to the regular tiling r, q see in Tables 9.1 and 9.3 many such decorations. 

We list here some operations transforming a map M into another map M.  

Truncation and capping The truncation of M at a vertex v of degree m consists of replacing the vertex t by a m-gonal face. The capping is, in a sense, dual to truncation, it consists of adding a new vertex v to a face F of M such that v is adjacent to all vertices of F, i.e. putting a pyramid on F. 

The truncation of M, respectively, capping of M consist of performing truncation, respectively, capping of all vertices, respectively, faces of M. The t-capping of M is obtained by the capping of t distinct faces of M. The b-cap cfM is the map obtained by capping all fe-gonal faces of M. 

4-triakon The A-triakon of a 3-gonal face F of M is obtained by partitioning F into three 4-gons according to the scheme below  

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