The pentagon valve does not exist. You have to use the star valve in both locations (star and pentagon). This is somewhat tricky, I think I wouldn't be able to do this without the hints from this forum.
Agreed. I think there should be some sort of hint for this. Something like Lacie saying "I don't think there are any more valves around... maybe something else will fit here?".
Otherwise I'd just keep searching for it and think I'd missed it.
