Within games development the process of geometric theory is a way to model objects or characters within a game. The way this is performed is through a design process using an initial mesh which gives the basic shape of an object to later be built upon with different textures.
When using polygons to create a mesh for a game, correct shapes must be determined both for correct design and for fluid movement should the shape be used for a moving character. In order to do this, different shaped polygons can be combined to create a new shape. For example the triangle polygon is widely used in combination with others to create more squared or kited shapes and can be used for more fluid movement. As a mesh is created polygons are steadily joined together by each vertice until a shape is complete with no vertices detatched from any other. This rule applies to both characters and objects within a game as not doing this would leave a split in the created item, leading it to not be whole. Once the 2D polygons have all been joined together into their desired shape with no vertices left detatched, the shape that is created becomes a 3D model composed entirely of 2D polygons. Below is an example of a full formed 3D character mesh made from 2D polygons. The character in the image is a monster from the PC video game Amnesia: The Dark Descent.
As you can see in the above image, the mesh of this character is made up nearly entirely of quad polygons. Though in order to round off the shape in the eye area, triangle polygons have been used in places to smooth out the shape and make it fit easier so that other polygons do not pierce each other or leave gaps in the mesh and push the body out of its desired design.
