I see many 'crystallized' style logos, for example the Sketch logo or something like the attached. What is this design style called?
There are 2 terms that describe this artwork:
Flat Low Poly
A search on Youtube brings similar results to your example. https://www.youtube.com/results?search_query=flat+low+poly+logo
Here is another example of it being called "Low poly." https://www.youtube.com/watch?v=G3NoCw43fb0
Flat Geometric Design
This Youtube video shows a similar result and calls it a flat design geometric pattern.
Bill Gardner, a logo designer and the creator of the website LogoLounge, publishes an annual review of the trends in logo design that he has identified over the course of the past year. In 2008, he identified a trend that he called "Facets." Here are the examples he provided:
In his 2014 trend report, he includes "Flat Facets"
His 2014 description of the trend reads, in part:
Another equally prolific line of trends over the last few years has been the facet. Watching this particular technique rocket and split into a variety of interpretations embraced by the design community has proven it has legs. This year's report identified four emerging strains, including Facet Fields, Crystals, Type Facets and Flat Facets, which we'll expound on here.
I think the terms "Facets," or "Crystals" probably best fit the images you linked in your question, but you could also investigate the other terms he uses in the quoted text.
In the arts it is simply called "geometric" shapes, the simplicity of the overall look is called "minimalism"...if you go on google and simply search for those 2 you'll find a bunch more like it.
It's "low poly" , minimalism can be everything and a list of combination of every logo type doesn't help you. search for "low poly" and your happy
It's typically called "geometric" design but can also be referred to as "low poly" because of it's roots in game design.
There are a few basic styles.. those land more in the Combination Marks since they have a symbol and text.
Lettermarks = Also words, but typically just Initials