Real Dictionary

plane
countable noun: A plane is a flat, level surface which may be sloping at a particular angle.
countable noun: A plane is a vehicle with wings and one or more engines, which can fly through the air.
singular noun: If a number of points are in the same plane, one line or one flat surface could pass through them all.

plane in American English 1
a surface that wholly contains every straight line joining any two points lying in it
flat; level; even
adjective: flat or level, as a surface
intransitive verb: to glide or soar
noun: a flat or level surface

plane in American English 2
to soar or glide
intransitive verb: to work with a plane
noun: any of various woodworking instruments for paring, truing, or smoothing, or for forming moldings, chamfers, rabbets, grooves, etc., by means of an inclined, adjustable blade moved along and against the piece being worked
transitive verb: to smooth or dress with or as if with a plane or a planer

plane in American English 3
a carpenter's tool for shaving a wood surface in order to make it smooth, level, etc.
to make smooth or level with or as with a plane
noun

plane in American English 4
any of a genus (Platanus) of trees of the plane-tree family having maplelike leaves, spherical dry fruits, and bark that sheds in large patches; sycamore

plane in British English 1
to fly without moving wings or using engines; glide
adjective: level or flat
noun: a flat surface in which a straight line joining any two of its points lies entirely on that surface

plane in British English 2
to level, smooth, or cut (timber, wooden articles, etc) using a plane or similar tool
noun: a tool with an adjustable sharpened steel blade set obliquely in a wooden or iron body, for levelling or smoothing timber surfaces, cutting mouldings or grooves, etc

plane in British English 3
noun