For the sake of simplifying what was said above to the casual forum browser without intensive modelling knowledge, I broke this down:
Basic 3d-
Face: A flat surface on a 3d model.
Vertex: A point which when connected with other vertices, creates a face.
Edge: A connection between two vertices.
When modelling-
Polygon(Poly): the method of which vertices are connected on a face. There are three types of polygons.
Triangle(Tri/Tris): When a face is broken down into triangles, so a face with four vertices will have two triangles, like a square with a diagonal line.
Quadrillateral(Quad/Quads): When a face is broken down into sections with four edges, squares and rectangles being simple examples.
N-Gons: Polygons with more than 4 edges, cylinders with a single polygon for end caps is an example of this, often have 5 to 16 edges.
Typically, high polygon modelling uses mostly quads, with some tris and n-gons for certain situations. Low polygon modelling almost always uses strictly quads, with some tris, and a game resolution model will be tessellated (have its vertices connected) into tris, so a model made of quads or n-gons will automatically be reformatted into all tris.
Bried UV mapping explanation:
UV mapping is the process of cutting a 3d model (sometimes called a mesh) along its edges in order to flatten it into a 2d image. This 2d image is then used to bake textures, create a diffuse texture, etc. and is automatically portrays on the 3d version of the model because it saves the UV data (basically the position of the polygon or face on the 2d image, and the file path of the image in certain model formats) for each polygon. Better explanations of this can be seen through simple UV mapping tutorials on youtube.
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