Projective and affine planes can be viewed as special kinds of designs. The following functions convert between designs and planes.

Design(P) : Plane -> Dsgn, SetIncPt, SetIncBlk

The design corresponding to the points and lines of the plane P.

The affine plane corresponding to the incidence structure D.

The projective plane corresponding to the incidence structure D.

> sds := SingerDifferenceSet(2, 3);
> sds;                             
{ 0, 1, 3, 9 }
> sdv := Development(sds);
> sdv;
2-(13, 4, 1) Design with 13 blocks
> spp := ProjectivePlane(sdv);
> spp: Maximal;
Projective Plane of order 3
Points: {@ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 @}
Lines:
    {0, 1, 3, 9},
    {1, 2, 4, 10},
    {2, 3, 5, 11},
    {3, 4, 6, 12},
    {0, 4, 5, 7},
    {1, 5, 6, 8},
    {2, 6, 7, 9},
    {3, 7, 8, 10},
    {4, 8, 9, 11},
    {5, 9, 10, 12},
    {0, 6, 10, 11},
    {1, 7, 11, 12},
    {0, 2, 8, 12}
> Universe(Support(spp));
Residue class ring of integers modulo 13