Papírové modely

Abstract

Paper models and cut-outs have been in our world for a long time and they are useful for the development of imagination. This thesis focuses on mathematics in models and on making nets (unfolded polyhedrons) of these models. The main part of this thesis describes how to decompose an object (asurface of a polyhedron) to its net and to describe mathematical procedures which enable us to do so. Suppose we have a body which we plan to decompose. Firstly, we check whether the faces of the body are really faces. Then we find out which faces are adjacent. Finally, we make a graph of the net of the body and decompose the body to a plane drawing. In the thesis, graph theory is mentioned often. This is due to the fact that individual body faces can be represented by graph vertices and graph edges correspond to the body edges the faces share. The second basic is analytical geometry, which is needed when rotating the faces into one plane.