Cremona-Richmond configuration

The Cremona-Richmond configuration, or the doily, is a configuration and generalized quadrangle.

Duads and systhemes
The can be constructed from a system of duads and systhemes from an alphabet of 6 characters,. A duad is a set of two distinct elements from. With an alphabet of size 6 there are 15 duads corresponding to the vertices of the. A systheme is a maximal set of duads such that each pair of duads is disjoint. With a alphabet of size 6 there are 15 systhemes each containing 3 duads. Permutations on are homomorphisms on the configuration forming its automorphism group. They are trivially transitive on its flags and thus the is regular.

The is the smallest non-trivial configruation which can be constructed this way (the smallest being the triad). The next smallest is a configuration of type.