A mineral that splits along a flat surface in 3 directions is said to have three cleavage planes.

This doesn't tell us the specific mineral, as many minerals exhibit cleavage. To identify the mineral, you'd need more information, such as:

* Cleavage angle: The angle between the cleavage planes.

* Cleavage quality: How well-defined and smooth the cleavage is.

* Other properties: Color, streak, hardness, luster, etc.

However, some examples of minerals with three cleavage planes include:

* Galena: Perfect cubic cleavage (3 planes at 90 degrees)

* Calcite: Perfect rhombohedral cleavage (3 planes not at 90 degrees)

* Fluorite: Perfect octahedral cleavage (4 planes, but 3 of them are visible at once)

Let me know if you have more information about the mineral in question and I can try to narrow it down further.