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If I want to speak of North, South, East, West in a general sense I could, for example, use the term cardinal direction.

Which term is appropriate to sum up horizontal and vertical in the same manner?

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Can you add more context please? Orientation, direction, extension, and others could or could not work depending on context. –  RegDwigнt Aug 30 '12 at 11:27
    
@ЯegDwight, thanks for editing. I have objects that are able to move vertically or horizontally within a plane area. I want to remember the status for the current moving object. Since the only states will be horizontal and vertical I need a name which generalizes those two words. I will go for axis or commonaxis in this case, as suggested by Joel Brown in his answer. Thanks for your effort. –  Aufwind Aug 30 '12 at 11:43

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up vote 2 down vote accepted

Depending on the context, you might use axis or orientation (credit: RegDwight).

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