ABSTRACT
A 3-(20,4,1) design is 3-hypergraphical if its point-set is represented as the twenty triplets in a 6-element set X, and its block-set is a union of orbits of four triplets under the action of Sym(X). There are precisely four distinct 3-hypergraphical 3-(20,4,l) designs; these have a number of interesting properties, of which the following is remarkable. There exists an intersection-reversing permutation of the triplets in X, which acts as an automorphism of two of our designs and as an isomorphism between the other two. We also give some general results on hypergraphical t-wise balanced designs.
