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DESCRIPTION OF THE STRUCTURE OF TEXT FORM CATALOGUE OF ARCHIMEDEAN SOLIDS
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HEADER
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GENUS: 
  genus of Archimedean solids in the list
NUMBER OF RECORDS: 
  number of all maps obtained as the result of the program. Note that records are sorted by the local type (as a primary key)
NUMBER OF MAPS:
  number of isomorphism classes with respect to (full) automorphism group of the map
REFLEXIBLE MAPS:
  number of reflexible maps
CHIRAL MAPS:
  number of chiral maps (chiral pairs). Note that there are (at least) two records in the list, both are considerate as
  one map (belongs to the same isomorphism class) 
#TYPE I:
  number of Archimedean maps of type I. Note that a map M of Type I may admit a vertex-transitive action 
  of $G\leq Aut(M)$ such that $G^+$ acts with two orbits on vertices 
#TYPE II:
  number of Archimedean maps of type II 
CAYLEY MAPS: 
  number of maps with trivial vertex stabiliser. 
NON-CAYLEY MAPS:
  appears only if some such maps have been found. Number of such maps.
ISOMORPHISMS:
  list of isomorphism classes, every record belongs to exactly one class
Representatives:
  indexes of representatives of isomorphism classes. May be used for quick search of the record (see below)
Classes:
  lists of indexes grouped by isomorphism classes.

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RECORD
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MAP:
  an unique identifier of the record. The form An.g means that map is 'A'rchimedean, with unique integer identifier 'n'
  and this map is of genus 'g'. This identifier may be used for quick access to the record.
NOTES:
  description of properties, may contain the link to the record of representative of the isomorphism class or the word
  'representative', information about the type of a map (depends on isomorphism class), information about reflexibility
  and information whether a particular map is Cayley or not. The line contains the information how can be the
  Archimedean map constructed from a regular map of given genus. The regular maps were classified by M. Conder
  (http://www.math.auckland.ac.nz/~conder/). The construction can be done using "map operations" introduced on the SIGMAP
  conference in Oaxaca (June, 2010). The respective regular map M is marked by Schlafli symbol - "{k,m}", where k,m are
  positive integers, k - valency of a vertex of M and m - valency of a face of M. The operations are denoted by the
  following abbreviations:

  * {k,m} - Archimedean map is a regular map,
  * Dual(M) - dual map of M,
  * Trun(M) - truncation of M,
  * Med(M)  - medial of M,
  * Med2(M) - medial of medial of M,
  * Snub(M) - diagonalised medial of medial M (for every edge in M there exist a quadrilateral face of Med2(M) which is
    subdivided into two triangles, there exist two chiral enantiomorphs, here they are counted as one map -- see also
    snub cube, snub dodecahedron among spherical Archimedean solids),
  * TDual(M) - truncation of dual map of M,
  * DBar(M)  - dual of the barycentric subdivision of M,
  * DMed(M)  - dual of the medial of M,
  * TDMed(M) - truncation of the dual of the medial of M.

  The information is introduced by the words 'isomorphic to', since the action of the automorphism group of the map
  `Ag.i` and action of automorphism group of the map given by respective construction from the regular map `{k,m}` 
  may not be the same.
QUOTIENT:
  full information about the quotient map on the surface S_gamma (see the paper) in terms of darts. If you want to
  construct faces of the quotient map, you should consider the cycles of length one of the respective permutation R*L.
ORBIFOLD:
  the signature of the respective orbifold
EMBEDDING:
  the way how the quotient map is embedded into the respective orbifold, the distribution of branch indexes
vertices: the distribution of batch point 'in vertexes'
daces: the sorted list of brach indexes distributed among faces. You must follow the cycle structure of R*L (above),
including one-cycles as well.
UNIGROUP:
  the presentation of covering transformation group read from the embedding of the quotient into the respective orbifold
SCHREIER VEC.: Schreier vector
  useful, if you want to draw the map, the cyclic sequence of generators of the automorphism group around the vertex
CTG (small): 
  the respective code of the covering transformation group in Small Group Library (see Magma, GAP). Note that a
  covering transformation group is the subgroup of the respective group of orientation-preserving automorphisms of
  a map.
CTG (fp): 
  the presentation of covering transformation group obtained by factorisation of UNIGROUP. Note that Tieze
  transformation were applied, sometimes it happened that the presentation is not beautiful, but it is checked to be
  correct.
LOCAL TYPE:
  self-explanatory, it is written in expanded form, not as Cundy-Rollett symbol
#DARTS:
  number of dart of lifted Archimedean solid, this may be helpful, if you want to construct the map in terms of R, L, as
  written below:
R:
  rotation of the Archimedean solid
L:
  dart-reversing involution of the Archimedean solid
 

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CHANGELOG
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- Wed Nov  9 15:29:30  CET 2011 : the correction of field names (covering transformation group, not the automorphism group!)
- Mon Oct 18 15:33:34 CEST 2010 : small correction of text about Type I
- Tue Jul  6 13:57:20 CEST 2010 : description expanded, some fixes done 
- Mon May 10 20:33:30 CEST 2010 : first version of the description
- Mon May 10 17:04:18 CEST 2010 : file created