Whether using the installer or the styles ZIP, many files from the Lemmings Plus VI styles are missing.
Basement: Folders are present, but are all empty. Theme.nxmi is missing.
Bridge: Folders are present. Objects and backgrounds are empty; most terrain pieces are present but a few are missing. Theme.nxmi is missing.
Garden: At a quick glance, does not appear to have any problems. I did not fully check if every file is present, though.
I've attached a copy of the styles to this post, both to assist with fixing this bug and as a workaround for anyone affected by it (as the styles are no longer included with the LPVI download).
