How to understand planes of cleavage in a rock?

a point of order: Rocks don't show "cleavage" unless one counts "hacky". Cleavage, in the technical sense, is a specific characteristic of "minerals". Cleavage is not the same as crystal form--a very common mistake especially with fluorite and calcite which cleave into perfect octahedron and rhombohedrons (rhombs for short) respectively.

Each mineral has its cleavage data published in its "mineral data description". First is the "type" of cleavage seen in the mineral. (See this link for an extensive description)

http://www.minerals.net/resource/property/cleavage...

NOTE: cleavage is NOT related to the crystal habit, as you will see in your reading. It results from a "natural line of RELATIVE weakness based on the pattern of chemical bonding and cross bonding in the mineral". Nor should it be confused with a mineral's "hardness". Fluorite has a cubic crystal habit but 4 cleavage planes which form a octahedron when cleaved twice along each of the 4 planes for a total of 8 planes

One of those types of cleavage is called "perfect". When cleavage is "perfect" it will state 2 additional items of information: the number of cleavage planes in that mineral (calcite has three) and the angles of the cleavage planes with respect to the a,b,c crystal's axis also. For contrast the mineral Muscovite--a mica sheet silicate, has "perfect" cleavage but only in one plane which is 90° (perpendicular) to the primary axis of its crystal).

(NOTE: The Miller Index expressed by 0s and 1s enclosed in brackets e.g [ 0 1 1] or [1 1 1] is related to crystal form and angle--which is another question)

As with the case of calcite rhomb, one doesn't count all the 6 separate sides as 6 separate planes. Each opposite end of the rhomb is the same cleavage plane ( not the same physical plane geometry-wise) In many of the links that I've provided there are diagrams which show different cleavage planes in detail and the shapes left when the sample is fully cleaved. A picture is worth a lot of talking and a video is even better so I've included a YouTube video on "calcite cleaving". Enjoy!

there can be many and complicated crystal arrangements of atoms

a plane is a surface that defines regular arrangementss

look up pictures o f 3-D crystals if there is an "easy direction to slide " or split that is the cleavage line for the large scale crystal

glass is a mix and does not have a preferred direction A diamond is very hard but if hit in the right place and angle it makes those lovely faces

good question