The Dressian Dr(3,8)

This page complements the paper: Sven Herrmann, Michael Joswig, and David Speyer: Dressians, Tropical Grassmannians, and Their Rays, 2012.

The Dressian Dr(3,8) has f-vector:

(1; 15,470; 642,677; 8,892,898; 57,394,505; 194,258,750; 353,149,650; 324,404,880; 117,594,645; 113,400).

Modulo the natural Sym(8)-symmetry, the f-vector reads:

(1; 12; 155; 1,149; 5,013; 12,737; 18,802; 14,727; 4,788; 14).

For a detailed description and discussion we refer to the aforementioned paper; this page lists some of the data derived from our computation.

All data is provided in xml format and the files can be read directly (using the load_data command) with the software system polymake, which we also used for the computations.

Here you find a list with all rays of the Dressian Dr(3,8). The file contains a Matrix<Int> object whose columns give coordinates for the rays:
all rays

For all cones starting from dimension two, we give one cone per orbit and additionally the size of the orbit. A cone is represented by the indices of its rays and the indices refer to the rows of the ray matrix above. Each file contains one object of type Array<Pair<Set,Int>> mapping each cone to its orbit size:
dimension 2
dimension 3
dimension 4
dimension 5
dimension 6
dimension 7
dimension 8
dimension 9

If you have any questions regarding the data, please contact Sven Herrmann.