I've been playing around with hexagons of late.

The first is, i suppose, hooh4oHHo&#tq. H here is q*h = sqrt(6). It's a bevelled square prism, such that the top and bottom become squares, the vertices being on the mid-points of the original squares, and the rectangles are converted into hexagons.

As a vertex figure, this leads to a tiling, with four {4,6} and two {6,4} at the vertex, and eight hexagon-prisms, which serve to connect {6,4}, in pairs.

I have not walked enough of this figure as yet, but the edge is quite large: it's nearly four times the edge of {5,4}, for instance.