Hinged dissections exist. Abbott, T. G., Abel, Z., Charlton, D., Demaine, E. D., Demaine, M. L., & Kominers, S. D. In Proceedings of Symposium on Computational Geometry (SoCG), pages 110-119, 2008.
Hinged dissections exist [link]Paper  bibtex   
@inproceedings{ dblp3134751,
  title = {Hinged dissections exist},
  author = {Timothy G. Abbott and Zachary Abel and David Charlton and Erik D. Demaine and Martin L. Demaine and Scott D. Kominers},
  author_short = {Abbott, T. G. and Abel, Z. and Charlton, D. and Demaine, E. D. and Demaine, M. L. and Kominers, S. D.},
  bibtype = {inproceedings},
  type = {inproceedings},
  year = {2008},
  key = {dblp3134751},
  id = {dblp3134751},
  biburl = {http://www.dblp.org/rec/bibtex/conf/compgeom/AbbottACDDK08},
  url = {http://doi.acm.org/10.1145/1377676.1377695},
  conference = {SoCG},
  pages = {110-119},
  text = {SoCG 2008:110-119},
  booktitle = {Proceedings of Symposium on Computational Geometry (SoCG)}

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