What is the name of this art?
What key words could I google to find similar results?
(Photos credit: The Mesh app on the Apple store )
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This is a relatively new trend in graphical design which is known as low poly design or low polygon design. If you google "low poly design" you'll find plenty of tutorials on how to produce such pictures by yourself (e.g. this one). In (very) short, you take a picture, triangulate it and generates the polygons out of your the induced mesh. Clearly, this is all done by computer. (Somewhat this remembers me of the painting style named cubism.)
While the images you provided are most likely computer-generated or digital paintings, there is a traditional craft that can achieve similar results.
Some papercrafting models use a similar concept of simplifying objects into geometric planes.
Sometimes this type of papercraft is specifically called a paper model, distinguishing it from other crafts such as origami.
The designs for them may even be done using digital software to start. Certain programs allow you to convert a 3D model into directions/steps for making a tangible paper model.
The best search terms to get results like these are
papercraft model or more specific things like
papercraft animals. You can find images, and also templates/instructions.
If you search
3D papercraft, you may get even more results in your style. Here's an article about artist Wolfram Kampffmeyer’s, including some of his beautiful creations, which are actually made from cardboard. Perhaps my favorite, and one closest to your images, is this wonderful red fox:
The style is indeed usually referred to as 'low-poly', but to nuance the accepted answer a little, 'low poly design' refers to a specific type of 3D modeling in which it is the expressive goal of the modeler/artist to create models with a low polygon count (i.e. with as few possible triangular faces).
It became more popular ever since more possibilities for small game companies to produce games became available. Since smaller companies have less resources to spend on the creation of advanced 3D models, they often revert to using low-poly models: they are created more rapidly, and they need less powerful 3D engines to render them - which also makes them more suitable for mobile games, for example.
That is not to say those 3D models cannot be a form of expression, or that they're easily created, since more information has to be communicated through less detail.
The low-poly style has immense popularity, and games like Minecraft famously make use of (a different but nonetheless) low-poly style.
So, while 'low-poly design' is an intentional variant of the style you're looking for, there are other ways to achieve a 'low-poly style'.
One can 'decimate' (reduce the vertex/polygon count on, like in Blender) existing models (including photogrammetric models) to create a similar look. While the look (depending on the method used) may not be aesthetically optimized (unequal distribution of polygons, strange displacements, &c.), it can easily and quickly be used on any model (import -> modify), including (pre)posed ones, and this is likely the technique used for the second of your example pictures, the lion/cheetah/jaguar, as it doesn't seem to have a symmetrical design (meaning it was likely a high-poly model in this specific pose before it was converted to a low-poly one).
To get back to your question, the "creation technique" could indeed be low-poly design, but this cannot really be concluded from your examples alone.
To find similar results, 'low-poly'; 'low polygon' - or even simply 'polygon'; 'polygonization'; 'delaunay';
The artist Davide Quayola has created polygonized artworks based on traditional mediums, such as painting:
Davide Quayola - Iconographies series (source)
Davide Quayola - Laocoön (source)
And the artist Matthew Day Jackson has used it in some of his works:
Matthew Day Jackson - The Way We Were (source, photo by Ed Jansen)