## 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 = 6, rank = 3 (dimension = 2)

List of the 17 representatives of IC(6,3), ordered by the RevLex-Index.
The numbers above the signs indicate the elements of the corresponding basis.

11121121231121231234
22332334442334445555
34445555556666666666
IC(6,3, 1) = +++++++++++++-++--++
IC(6,3, 2) = ++++++++++++++++++--
IC(6,3, 3) = +++++++++++++++++++-
IC(6,3, 4) = ++++++++++++++++++++
IC(6,3, 5) = 0++++++++++++++-+---
IC(6,3, 6) = 0+++++++++++++++++--
IC(6,3, 7) = 0+++++++++++++++++++
IC(6,3, 8) = 0++++++++++++++++++0
IC(6,3, 9) = 0++++++0+++++++++---
IC(6,3,10) = 0++++++0++++++++++--
IC(6,3,11) = 0++++++0+++++++++++-
IC(6,3,12) = 0++++++0+++++++0++--
IC(6,3,13) = 0++++++0+++++++0+0--
IC(6,3,14) = 0++++++0++++++0-+---
IC(6,3,15) = 0000++++++++++++++++
IC(6,3,16) = 0000++++++++++++0+++
IC(6,3,17) = 0000000000++++++++++