Strictly Thin Edges in Bricks and Braces

A brick is solid if and only if its underlying simple graph is solid. A brick or brace has a specified simple matching covered graph J as a matching minor if and and only if its underlying simple graph has J as a matching minor. As these examples show, the properties of bricks and braces that are of interest to us are mostly those which are enjoyed by simple bricks and braces. This, as explained below, brings into question the efficacy of using thin edges as inductive tools for establishing properties of bricks and braces.