3D computer graphics use three axes (x, y, and z) instead of just two to represent 3D coordinates. The basic object used in 3D mesh modeling is a vertex, and connecting vertices with lines creates edges. The simplest polygon is a triangle formed from three vertices connected by three edges. Groups of connected polygons form a mesh, which can be rendered as 3D models. Meshes should be non-self-intersecting without duplicated vertices or faces to appear appealing when rendered.

1. Geometric Theory
Geometry
3D computer graphics provide work the same values discovered in 2D vector
artwork, but use a further axis. When conceiving 2D vector artwork, the
computer sketches the image by contriving points on X and Y axes (creating
coordinates) and connecting these points with paths (lines). The subsequent
forms can be filled with hue and the lines caressed with hue and thickness if
required.
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3D programs function on a grid of 3D co-ordinates. 3D co-ordinates are pretty
much the identical as 2D co-ordinates except there’s a third axis known as the
Z or ‘depth’ axis.

2. Geometric Theory and Polygons
The rudimentary object utilised in mesh modelling is a vertex, a issue in three
dimensional space. Two vertices attached by a directly line become an edge.
Three vertices, connected to each other by three borders, define a triangle,
which is the simplest polygon in Euclidean space. More convoluted polygons
can be created out of multiple triangles, or as a single object with more than 3
vertices. Four aligned polygons (generally referred to as quads) and triangles
are the most common shapes that are used in polygonal modelling. A group of
polygons, attached to each other by distributed vertices, is generally
mentioned to as an element. Each of the polygons making up an component is
called a face.
In Euclidean geometry, any three non-collinear points work out a plane. For
this reason, triangles habitually live a single plane. This is not necessarily true
of more convoluted polygons, although. The flat nature of triangles makes it
easy to determine their surface usual, a three-dimensional vector
perpendicular to the triangle's exterior. Surface normal's are helpful for
determining lightweight transport in ray finding.
A assembly of polygons which are attached by distributed vertices is
mentioned to as a mesh, often furred to as a wireframe model.
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In order for a mesh to emerge appealing when rendered, it is desirable that it
be non-self-intersecting, meaning that no edge passes through a polygon.

3. Another way of looking at this is that the mesh will not pierce itself. It is also
attractive that the mesh not comprise any mistakes such as doubled vertices,
edges, or faces. For some reasons it is important that the mesh be a manifold –
that is, that it does not comprise holes or singularities (locations where two
distinct parts of the mesh are attached by a lone vertex).
http://en.wikipedia.org/wiki/Polygonal_modeling
Primitives
In 3D submissions, pre-made things can be utilised to make forms out of
diverse forms, the most basic of this forms are the Standard Primitive things,
or the widespread Primitives, these forms alter from the rudimentary cube or
box to spheres, cylinders, pyramids (both triangular and rectangle founded)
and cones. They are utilised as the beginning point for modelling. They can be
revised one time created.
Surfaces
Polygons can be defined as specific surfaces and then have hue, texture or
photographic charts added to them to create the yearned gaze. The
demonstration below displays how a map is brandished as if the object has
been unwrapped.

4. http://goanna.cs.rmit.edu.au/~gl/teaching/Interactive3D/2012/images/uv-unwrap.jpg