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To give a general definition of the term "free surface" with reference to a solid, liquid or gas one can say that it is the surface where the superficial tension phenomena take place.
The superficial tension is the force that builds up on the interface layer (first layer of molecules at a certain interface, e.g first layer of water molecules at the interface air-water) that compress to huge pressures the phase that it surrounds.
Since gases do not exhibit superficial tension phenomena (they have no defined shape or volume) they can not form on their own a free surface. Instead they exhibit a free surface when in contact with liquids.
Liquids (they do not have defined shape but do have volume) have one well defined free surface and this is the surface that is perpendicular to the superficial tension force (that compresses the water molecules inside the fluid to huge pressures).
Solids (because they have both shape and volume well defined) have particles arranged very close in certain repetitive patterns. The interaction force between the solid atoms is huge, and they can not be further compressed by the superficial force at the interface with other phase (liquid or gaseous). In addition because of these huge interaction forces between they particles, solids can be cut in an infinite number of shapes and sizes. This is why we say that for a solid the number of free surfaces in infinite.
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