In this paper we determine the spectrum for octagon quadrangle systems [OQS] which can be partitioned into two strongly balanced 4-kitedesigns.

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Mercury’s Debussy Quadrangle (H14) lies between 0–90° E and 22.5–65° S. Here we use MESSENGER data to produce the first geological map of this quadrangle at a scale 1:3,000,000, based on linework completed 1:300,000. We distinguish crater units plains units. For compatibility with historic recent maps other Mercury quadrangles, global (Main Map), have made two versions map, craters classified a...

A Subiaco hyperoval in PG(2, 2h), h ≥ 4, is known to be stabilised by a group of collineations induced by a subgroup of the automorphism group of the associated Subiaco generalised quadrangle. In this paper, we show that this induced group is the full collineation stabiliser in the case h 6≡ 2 (mod 4); a result that is already known for h ≡ 2 (mod 4). In addition, we consider a set of 2h + 2 po...

A Kantor family is a collection of subgroups from which a generalized quadrangle can be constructed using Kantor ' s idea. This paper considers the case in which some of the subgroups in the Kantor family or its related family are normal in the ambient finite group G. We show that if two members of a Kantor family are normal in G then G is elementary abelian and that if all members of the relat...

An octagon quadrangle is the graph consisting of an 8-cycle (x1, x2, ..., x8) with two additional chords: the edges {x1, x4} and {x5, x8}. An octagon quadrangle system of order v and index λ [OQS] is a pair (X,H), where X is a finite set of v vertices and H is a collection of edge disjoint octagon quadrangles (called blocks) which partition the edge set of λKv defined on X. An octagon quadrangl...

In these notes we are interested in the following fundamental question: “Given a thick generalized quadrangle S(x) with elation point (respectively center of transitivity) x , when does the set of all elations about x form a group?”. It was the general belief for a long time that this is usually the case. However, the goal of these notes is to show that this belief is wrong. To that end, we wil...

An intriguing set of points of a generalised quadrangle was introduced in [2] as a unification of the pre-existing notions of tight set and m-ovoid. It was shown in [2] that every intriguing set of points in a finite generalised quadrangle is a tight set or an m-ovoid (for some m). Moreover, it was shown that an m-ovoid and an i-tight set of a common generalised quadrangle intersect in mi point...