Honeycomb structure shape. A honeycomb structure has hexagonal spaces and walls of some thickness. For a 2-dimensional surface, how can one determine what other shapes are possible(if any) and how would they be oriented to construct a symmetric(2-planes) mesh-like structure?

Any tiling of the (Euclidean) plane can be used to create a 3D sandwich simply by making each tile the cross-section of a prism and giving all the faces a finite thickness.

The regular hexagonal-prism "honeycomb" which you mention gives the greatest strength for the least material.

If you are interested in other more decorative tilings, the 17 wallpaper groups (mentioned in various comments) describe their possible symmetries. There is an infinite variety of specific tilings with these symmetries, from which honeycomb sandwiches can be derived. See for example the uniform tilings of the Euclidean plane, some of which have tiles of several different shapes. Or, hunt around for something that appeals to you, such as the Cairo tiling. If you feel ambitious, you could even go for an aperiodic tiling such as the Penrose tiling

More sophisticated sandwiches with walls which lean sideways are also possible, such as the spaceframe structure of alternating octahedral and tetrahedral cells.