We construct the Witt design D on 12 points, together with its point-set P and block-set B.
> D, P, B := WittDesign(12); > D; 5-(12, 6, 1) Design with 132 blocks
This design has a resolution; i.e. the block-set of D can be partitioned into parallel classes. In this example, the automorphism group A acts transitively on the classes of the resolution. Hence we can get the resolution of D by taking the orbit of a single parallel class under A. To construct the initial class, we select one of the blocks of points and then find the block consisting of the remaining points.
> b1 := B.1; // first block (arbitrary choice)
> b2 := B ! (Set(P) diff b1);
> class := {b1, b2};
> class;
{ {1, 6, 7, 8, 11, 12}, {2, 3, 4, 5, 9, 10} }
> A, PP, BB := AutomorphismGroup(D);
> resolution := Orbit(A, PP, class);
> #resolution;
66
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