A previous post mentioned that 25 of the 28 Heesch types could be formed using only identical edges of central rotation. The other three can also be formed using edges of central rotation, but they require at least two sizes of edges. Edges formed with center-point rotation can serve not just as C edges in the Heesch classification of types but also as T, G, C3, C4, and C6 edges, that is, any type of edge.
Mirroring an edge formed with central rotation is equivalent to gliding it. Translating an edge that mirrors over its midpoint is also equivalent to gliding it. Hence, some edges that are translated or mirrored can be seen as glided. How many of the Heesch types can be formed with all edges that are glided whether or not the edge fits as a glided edge?
Glided edges have less flexibility than edges formed with center-point rotation partly because they must be paired and not all edges pair in types formed on triangular and pentagonal templates. The closest we can get to an all-glided version of a triangular type, for example, is shown below. Notice that it can satisfy the CGG type in two ways, but not three. This tiling satisfies CCC and CC6C6 as well as CGG.
Let us start with the two quadrilateral types that must be formed with glided edges, G1G1G2G2 and G1G2G1G2. Below is an example of G1G1G2G2 with matching pairs differentiated.