Polygonal modeling I believe is probably the most common approach for modeling 3D objects. The polygons approximate the model's surfaces using polygon mesh.
It's one thing to create a polygon model of an object in Blender for 3D printing. Animating a polygonal model is a different level requiring more computer processing.
Polygonal 3D animation goes all the way back to 1972. The short silent film A Computer Animated Hand produced by Edwin Catmull and Fred Parke was rendered on a 3D animation program Edwin Catmull created. According to Wikipedia the hand model was Catmull's left hand. A plaster model from a plaster-of-paris mold of his hand had 350 triangles and polygons drawn on it physically with ink. The coordinates of each of the corner points of the polygons and triangles on the hand model was recorded as digital data.
Further description of the film's production process can be found in the film's Wikipedia entry.
