## Catalog of Isomorphism Classes of Oriented Matroids

The following table shows the number of isomorphism classes of oriented matroids (where card is the cardinality of a simple representative). Data can be accessed by clicking on the corresponding number (if available):

 All Non-degenerate (Uniform)
card = 2 card = 3 card = 4 card = 5 card = 6 card = 7 card = 8 card = 9 card = 10
rank = 2 1 1 1 1 1 1 1 1 1
rank = 3 (dim = 2) 1 2 4 17 143 4 890 461 053 95 052 532
rank = 4 (dim = 3) 1 3 12 206 181 472 unknown unknown
rank = 5 (dim = 4) 1 4 25 6 029 unknown unknown
rank = 6 (dim = 5) 1 5 50 508 321 unknown
rank = 7 (dim = 6) 1 6 91 unknown
rank = 8 (dim = 7) 1 7 164
rank = 9 (dim = 8) 1 8
rank = 10 (dim = 9) 1

### Cardinality = 7, rank = 5 (dimension = 4)

List of the 25 representatives of IC(7,5), ordered by the RevLex-Index.
The numbers above the signs indicate the elements of the corresponding basis.

111112111121112112123
222233222332233233444
333444334443444555555
445555455556666666666
566666777777777777777
IC(7,5, 1) = +++++++++++++++++++++
IC(7,5, 2) = 0++++++++++++++++++++
IC(7,5, 3) = 0++++++++++0++-++-+--
IC(7,5, 4) = 0++++++++++0+++++++++
IC(7,5, 5) = 0++++++++++0++++++0++
IC(7,5, 6) = 00++++0++++++++++++++
IC(7,5, 7) = 00++++0++++++++0+-+--
IC(7,5, 8) = 00++++0++++++++0+++++
IC(7,5, 9) = 00++++0++++++++0++++0
IC(7,5,10) = 00++++0++++++++00+0++
IC(7,5,11) = 000+++00+++0+++++++++
IC(7,5,12) = 000+++00+++0++++++0++
IC(7,5,13) = 000+++00+++0++++++000
IC(7,5,14) = 000000+++++++++++++++
IC(7,5,15) = 0000000++++++++++++++
IC(7,5,16) = 0000000++++++++0+-+--
IC(7,5,17) = 0000000++++++++0+++++
IC(7,5,18) = 0000000++++++++0++++0
IC(7,5,19) = 00000000+++0+++++++++
IC(7,5,20) = 00000000+++0++++++0++
IC(7,5,21) = 00000000+++0++++++000
IC(7,5,22) = 00000000000++++++++++
IC(7,5,23) = 000000000000+++++++++
IC(7,5,24) = 000000000000++++++0++
IC(7,5,25) = 000000000000000++++++