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There is problem where you can not unfold faces of 3D object in a way were all plane sides stay connected with each other in 2D Euclidean space.

How this problem is named and how I can make reference to this impossibility in my thesis?

Timo
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  • Is http://erikdemaine.org/papers/Ununfoldable/ along the lines of what you're looking for? – Barry Cipra Apr 29 '17 at 13:36
  • @BarryCipra this is more advanced than I need. I mean that common sense where you can't make 3D object into 2D without cutting, slicing or deforming object. Do I even need to prove or reference this in thesis? – Timo Apr 29 '17 at 13:58
  • I guess I don't understand what you mean by making a 3D object into 2D "without cutting, slicing or deforming" it. – Barry Cipra Apr 29 '17 at 14:03
  • @Timo: Are you asking why (e.g.) the surface of a polyhedron is not isometric to a subset of the plane? – Andrew D. Hwang Apr 29 '17 at 14:12
  • If I read well your title, the fact that it is "in a MSc Thesis" should impact the way it is proven ? – Jean Marie Apr 29 '17 at 14:51
  • @AndrewD.Hwang It seems so I think.

    http://www.z-bit.eu/s/cutting-wrapping.png I work with project where user can put graphics on map which is then projected onto 3D object. User does understand that placing graphics over edge of the map will not be projected on object. But he may not be understanding why is it impossible to create projection map with sides intact and without distortion.

    Like why do we need use projection between higher and lower level spatial dimension?

    Sorry about my inadequacy in mathematical terms.

     – Timo Apr 29 '17 at 15:16
  • I think my approach to the problem isn't the best. I can reword some paragraphs to avoid proving what I wrote and you don't have to read my mind. Thanks anyway :) – Timo Apr 29 '17 at 15:46

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