This picture shows all the tilings/geometries you can select in the Geometry Experiment menu in HyperRogue 10.2. The first two columns show the truncated (more precisely, truncated dual, or chamfered) and non-truncated variant of each basic tiling. Some of these look the same; this is because the image also shows some quotient spaces -- look for the player character appearing in multiple places :) These are available in all lands -- as shown in the two columns on the right, using the Red Rock Valley as an example. There are more tilings available, but only in particular lands -- we already know the Warped Coast (fourth column), and the new land, the Crystal World, uses the dual tiling (we could previously play in the dual tiling in the Graveyard, but the Crystal World is much more explicit). (The Crystal World does not appear during the normal gameplay -- it is very simple and designed rather for geometry experiments.)
On the Steam forum, players have already started creating ideas about the possibilities for new lands specific to the octagonal tiling. Have fun!