• "{A,B,C,D}"
  where A,B,C and D are subsets of {1,2,3,4,5,6}. The matroid is the graphical matroid given by the multi-graph of a four cycle with edge repeated and named according to the four sets. Notice that the ordering of the sets is unimportant.
  Example:
  Matroid for "{1,2,346,5}"
  

  	1 2 3 1 2 4 1 2 5 1 2 6 1 3 5 1 4 5 1 5 6 2 3 5 2 4 5 2 5 6
  Graph	Bases

  We remind the reader that we go from a graph to a matroid by letting every spanning tree define a basis.
• "[A,B;C,D](E)"
  where A, B, C, D and E are subsets of {1,2,3,4,5,6}. The matroid is the graphical matroid given by a four cycle with a diagonal edge. Edges are repeated and named acoording to A, B, C, D and E. Here E corresponds to the diagonal edge while (A,B) and (C,D) correspond to the two paths connecting the two valency three vertices.
  Example
  Matroid for "[1,26;3,4](5)"
  

  1 2 3 1 2 4 1 2 6 1 3 6 1 4 6 2 3 4 2 3 5 2 3 6 2 4 5 2 5 6 3 4 6 3 5 6 4 5 6

• "Complete Graph Matroid"
  This text string represents a matroid of a complete graph. It only appears once in our drawings where the edges of the complete graph have names as given below.

  	1 2 3 1 2 4 1 2 5 1 3 4 1 3 6 1 4 5 1 4 6 1 5 6 2 3 4 2 3 5 2 3 6 2 4 6 2 5 6 3 4 5 3 5 6 4 5 6
  Affine point configuration	Bases

• A caterpillar tree is represented by a string of the form C(ab,...,yz) where the leaves ab and the leaves yz form cherries. The dots describes the leaves in between in order from ab to yz. Here the letters are all names of vertices of the tree, that is, numbers between 1 and 6.

Less generic planes in TP5

Dimension 9

Dimension 8

Dimension 7

Dimension 6

Software used for the computations