When people think of magic and spells and enchantments, one of the most intuitive concepts is that magic can change fortune. Associating magic with the ability to make things more or less likely is intuitive. An abstraction for an attribute describing how likely or unlikely something is to happen is a probability. Typically, a probability is thought of as something abstract and even intangible. It is not something that is thought of as being concrete. Anything that can be built from different elements or parts has probabilities associated with it. Imagine having a bucket of Lego blocks with different shapes you can build stuff from. Think of all the possible things that you could build. It is possible to arrange and connect those shapes in different ways to build different things. In other words, there are different possible combinations and ways you can configure the blocks to build different things. Now, whether you can build anything useful or not does not take away from there existing a possible and probable way to put things together so that you can make something nifty. In other words, there is some possibility and some probability of you being able to build something useful that you can touch with Lego blocks. That is analogous to energy and matter. Energy is fundamentally about possible ways that things can be arranged, and matter is just an aspect of that energy. So, correlated with how energy can be arranged is a probability and therefore correlated with how matter can be arranged is also a probability. So, if we take for granted that magic can alter probabilities, then we can also infer that magic can alter how particles in a solution can be arranged such that versus naturally falling to a low energy state, the structure of something can be forced into and kept in a high energy state. This will result in crystals being formed in different shapes than what they should likely be. In this case, alum crystals like to naturally form in octahedral shapes, so magic can be used to cause the crystals to grow in shapes that are not octahedral.
In the article Make Your Own Magical Rules, I explained how to create a magical ontology that contains a body of axioms from which different geometric shapes can be derived that corresponds to magical formulas you can create. In other words, the formula of your spell could have a higher-dimensional geometric shape. What underpinned that method were Abelian groups and fields. The shape of the magic can thus be treated as a field where that field can be magically projected into the solution of alum and water such that the water is enchanted. Since for every part of the solution, the particles will be influenced by the enchantment, you can treat it as a type of magical field interacting with the statistical properties of the solution so that how the crystals are formed are caused by the enchantment. In other words, what caused the crystals to be and thus what allows them to consequently exists is bound up in the magic that created them where this is also inherent in the physical energy of the crystal. It is important to note that crystals formed from an aqueous solution do evaporate in the open air, so after creating the crystals, you should also go back over them with a layer of something not water-soluble that puts a shell on them.
Below is the magical, geometric shape that was created in the article Make Your Own Magical Rules
This is what a crystal formed from that enchantment might look like: