Symmetry

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Basic

Axes of symmetry

Axes of symmetry have to do with balance of shape when rotated around these imaginary axes.
Every crystal belongs to a particular crystal system (cubic, tetragonal, hexagonal, trigonal, orthorhombic, monoclinic or triclinic) and the symmetry for each of these systems is defined by ideal shapes.

Following is an illustration of symmetry axes in the orthorhobic system.
When determining the axes symmetry it is important to rotate (or spin) the crystal around that axis through a 360° rotation and judge how many times the exact image is repeated during the rotation.

The basic form that makes up the orthorhombic system looks like a matchbox
Here the match box is represented as a prism with a pinacoid
An imaginary needle (axis) is pierced through the center of the top plane

We take an arbitrary plane as our starter for the rotation (the front plane in this case
During a 360° rotation of the prism around the axis, the exact same image is shown twice
The above process is repeated but now with the needle (axis) pierced through the pinacoidal faces

We take another arbitrary plane as our starter for rotation (the top plane)
Again during a 360° rotation of the prism around the axis, the exact same image is shown twice
The final axis of symmetry (in the orthorhombic prism) is through the front plane

We now take a pinacoidal face (the front plane) as the start of our rotation
And again, during a 360° rotation of the prism around the axis, the exact same image is shown twice
If one would place the matchbox on one of the pinacoidal faces, one would get identical results

As can be seen in the above images there are 3 axes of symmetry in the orthorhombic system and each axis produces the same image twice during a 360° spin around that axis.
When an axis shows the same image twice, we name it a 2-fold axis of symmetry (or better: a "digonal axis of symmetry"). So the orthorhombic system is characterized by 3 2-fold axes of symmetry.

Other crustal systems will have less or more axes of symmetry. A 3-fold axis of symmetry means that the image is repeated 3 times (named a "trigonal axis of symmetry") etc.

Planes of symmetry

Center of symmetry

Sources