Here's why:

* Orthorhombic Symmetry: Orthorhombic crystals have three different axes of symmetry (a, b, and c) with different lengths. This means the crystal structure is not cubic, and the planes are not all equivalent.

* Plane Families: The Miller indices {111} represent a family of planes. Each plane in this family is parallel to the others and has the same crystallographic orientation.

* Equivalent Planes: The equivalent planes are those that are related by the symmetry operations of the orthorhombic crystal system. These operations include:

* Rotations: 90-degree rotations around each of the three axes (a, b, and c).

* Reflections: Reflections across planes perpendicular to each axis.

Since there are three axes of symmetry, and each axis allows for two orientations (positive and negative), there are a total of 3 * 2 = 6 equivalent {111} planes in an orthorhombic crystal.