If you have been in the crystal community for a while, you’ve almost certainly heard of crystal systems. These are important in crystallography and are extremely useful when it comes to identifying certain minerals and classifying crystal properties.

But what are crystal systems? What are crystal structures? Crystal systems differ greatly, but each one defines crystals on symmetric points of their crystallographic axes. It will make more sense later, trust us. Crystal structures, on the other hand, are merely the arrangement of atoms that make up a crystal. There are seven crystal systems, but some would say six. Let’s get into that since defining structures and systems without examples can be a little confusing.

## 7 Systems (Some Say Six)

Whether there are six or seven is ultimately irrelevant. However, due to their similar relationship, some put trigonal and hexagonal in the same category.

We will say seven because we are going to define seven crystal systems. Since crystals are made up of multiple properties, we will have to break this up a little more.

If you’ve read our other gemstone blogs, you’ve probably seen us reference crystal systems before. The seven we reference are:

**Triclinic****Monoclinic****Orthorhombic****Tetragonal****Trigonal****Hexagonal****Isometric (Cubic)**

Each of these varies from another drastically, even at a surface level. A crystal must fit into one of these categories based on its crystal structure and symmetry.

Let’s use the isometric crystal system as a reference to show you how this stuff is defined. The isometric system is great for examples because it is extremely common and simple.

This is a simple cubic crystal system. It is extremely symmetric with four threefold axes. But what does that mean, exactly? Let’s break it down.

A crystal system is defined through rotational symmetry. That means if we rotate our cube by a certain amount, it is visually unchanged. **For reference, pyrite has a cubic crystal system, and it is a symmetrical stone.**

Now that we know our cube won’t look too different if we turn it around, we can talk about the elephant in the room. This X-fold axis thing isn’t as complicated as it sounds. Essentially, we can rotate something 360°/X times to get our rotational symmetry as an X-fold something.

Let’s start small. ** 2**-Fold. Take the letter S, for instance. This is our letter S.

Now, if we want to test if this has ** 2**-Fold symmetry, we’ll need to take 360°/

**= 180°. Ok, good. Now, what that means is, to prove it has**

*2***-Fold symmetry, we need to rotate that 180°. You can try that out. It’ll look basically the same.**

*2*Let’s try** 3**-Fold symmetry now. Take 360°/

**= 120°. That means we need to rotate something 120°, and if it looks the same, then it has 3-Fold rotational symmetry. A famous example of this is the triskelion.**

*3*If you rotate that, you will see it has 3-Fold rotational symmetry.

With those examples out of the way, we now have an idea of what that threefold rotational symmetry thing means. But you’ll notice that we said *four threefold axes*. You’ll also notice that crystals exist in the third dimension. What we’ve been showing you are 2D images.

Let’s show you a real cubic crystal.

Pyrite is naturally cubic. It has four axes of 3-fold rotational symmetry. But a cube also has three axes of 4-fold rotational symmetry. It also happens to have six 2-fold axes of rotational symmetry. **This all depends on the faces and axes that you are looking at.**

## Summary of Symmetry

As long as you understand this, it’s quite easy to visualize the symmetry of other systems.

**Triclinic –** None, three axes with unequal lengths. Examples, Rhodonite, Labradorite, Ajoite.

**Monoclinic –** One axis of two-fold symmetry. We can rotate the structure 180° without seeing variance in its appearance. Examples: Charoite, Chlorites, Diopside.

**Orthorhombic –** Three axes of 2-fold symmetry, meaning we can rotate the structure 180° from those three axes without seeing variance in its appearance. Examples: **Topaz, Olivine, Zoisite.**

**Tetragonal –** One 4-fold axis of symmetry. We can rotate the structure 90° without seeing variance in its appearance. Examples: **Rutile, Zircon, Ziroite.**

**Trigonal –** One 3-fold axis of symmetry. We can rotate the structure 120° without seeing variance in its appearance. Examples: **Galeite, Quartz, Cinnabar.**

**Hexagonal –** One 6-fold axis of symmetry. We can rotate the structure 60° without seeing variance in its appearance. Examples: **Zinc, Beryl, Ice, Graphite.**

**Cubic –** Four 3-fold axes of symmetry. We can rotate the structure 120° from those four axes without seeing variance in its appearance. Examples: **Garnet, Pyrite, Fluorite.**

**Now, we have to give full disclosure. This is only scratching the surface of the complexity of crystal systems.** Within each of these systems are crystal classes which add more variety to them. Each of these classes has its own properties that make them substantially different from the others.

So, while crystals are classified into 7 different crystal systems, there are many more crystal classes and many varieties of crystals and families of crystals. There are also planes, mirrors, and other variables that define why a crystal belongs to a certain crystal system. We’re really only giving you the basics.

Many of these are related in certain ways, such as the crystal structure being the arrangement of atoms that define a crystal, which, in turn, helps define its crystal system. This can be further divided into sets of unit cells (which is what we talk about most when we define the rotational symmetry, not the entire crystal itself). When we look at a crystal structure, we look at the symmetry to define its crystal system.

## The Wrap Up

Crystal Systems are very complex. There is a lot of analysis and geometry that goes into defining a crystal. But there’s so much more to defining a crystal. There are light properties, hardness, color, lustre, chemicals, lattice systems, and more.

But crystal systems aren’t a bad place to start. Take your favorite crystal and look it up. What crystal system does it have? Is it symmetrical? Not very symmetrical at all? Well, no matter the answer, we thank you for reading!

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