## Catalog of Isomorphism Classes of Oriented Matroids

The following table shows the number of non-degenerate (uniform) 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 1 1 4 11 135 4 382 312 356
rank = 4 (dim = 3) 1 1 1 11 2 628 9 276 595 unknown
rank = 5 (dim = 4) 1 1 1 135 9 276 595 unknown
rank = 6 (dim = 5) 1 1 1 4 382 unknown
rank = 7 (dim = 6) 1 1 1 312 356
rank = 8 (dim = 7) 1 1 1
rank = 9 (dim = 8) 1 1
rank = 10 (dim = 9) 1

### Cardinality = 7, rank = 3 (dimension = 2)

List of the 11 non-degenerate (uniform) representatives of IC(7,3), ordered by the RevLex-Index.
The numbers above the signs indicate the elements of the corresponding basis.

11121121231121231234112123123412345
22332334442334445555233444555566666
34445555556666666666777777777777777
IC(7,3, 1) = +++++++++++++++++++-++++++++-----+-
IC(7,3, 2) = +++++++++++++++++++-++++++++--+----
IC(7,3, 3) = +++++++++++++++++++-+++++++++-+----
IC(7,3, 4) = ++++++++++++++++++++++++++--++--+++
IC(7,3, 5) = ++++++++++++++++++++++++++-+++--+++
IC(7,3, 6) = +++++++++++++++++++++++++++++-+----
IC(7,3, 7) = +++++++++++++++++++++++++++++-++---
IC(7,3, 8) = +++++++++++++++++++++++++++++-+++--
IC(7,3, 9) = +++++++++++++++++++++++++++++++++--
IC(7,3,10) = ++++++++++++++++++++++++++++++++++-
IC(7,3,11) = +++++++++++++++++++++++++++++++++++