Tutte polynomials of q-cones

We derive a formula for the Tutte polynomial t(G′;x,y) of a q-cone G′ of a GF(q)-representable geometry G in terms of t(G;x,y). We use this to construct collections of infinite sequences of GF(q)-representable geometries in which corresponding geometries are not isomorphic and yet have the same Tutte polynomial. We also use this to construct, for each positive integer k, sets of non-isomorphic GF(q)-representable geometries all of which have the same Tutte polynomial and vertical (or Whitney) connectivity at least k.