3D models are most-often represented as triangulated polyhedra forming a triangle mesh. Non triangular surfaces can be converted to an array of triangles through tessellation. Attributes from the vertices are typically interpolated across mesh surfaces.
The vertices of triangles are associated not only with spatial position but also with other values used to render the object correctly. Most attributes of a vertex represent vectors in the space to be rendered. These vectors are typically 1 (x), 2 (x, y), or 3 (x, y, z) dimensional and can include a fourth homogeneous coordinate (w). These values are given meaning by a material description. In realtime rendering these properties are used by a vertex shader or vertex pipeline.
Such attributes can include:
2D or 3D coordinates representing a position in space