Paper by Erik D. Demaine

Reference:

Erik D. Demaine and Joseph O'Rourke, “Computational Geometry Column 37”, International Journal of Computational Geometry and Applications, volume 10, number 1, February 2000, pages 103–107. Also appears in SIGACT News, volume 30, number 3, issue #112, September 1999, pages 39–42.

BibTeX

@Article{CGcolumn37,
  AUTHOR        = {Erik D. Demaine and Joseph O'Rourke},
  TITLE         = {Computational Geometry Column 37},
  JOURNAL       = {International Journal of Computational Geometry and
                   Applications},
  JOURNALURL    = {http://www.worldscinet.com/ijcga/ijcga.shtml},
  VOLUME        = 10,
  NUMBER        = 1,
  MONTH         = {February},
  YEAR          = 2000,
  PAGES         = {103--107},
  NOTE          = {Also appears in SIGACT News, volume 30, number 3,
                   issue \#112, September 1999, pages 39--42.},

  length        = {4 pages},
  doi           = {https://dx.doi.org/10.1142/S0218195900000073},
  dblp          = {https://dblp.org/rec/journals/ijcga/DemaineO00},
  comments      = {This paper is also available as
                   <A HREF="http://arXiv.org/abs/cs.CG/9908007">
                   arXiv:cs.CG/9908007</A> of the
                   <A HREF="http://arXiv.org/archive/cs/intro.html">
                   Computing Research Repository (CoRR)</A>, and from <A HREF="https://doi.org/10.1142/S0218195900000073">ACM</A>.},
  updates       = {I understand that Kasturi Varadarajan's problem (is there
                   a topological cube with orthogonal opposite facets?)
                   has been solved by
                   <A HREF="http://www.math.tu-berlin.de/~ziegler/">G&uuml;nter
                   Ziegler</A>.
                   <P>
                   John Conway's Holyhedron Problem has been solved
                   by Jade Vinson in
                   &ldquo;<A HREF="http://springerlink.metapress.com/app/home/contribution.asp?wasp=2g5ltmvyrp1wf0guubex&referrer=parent&backto=issue,5,8;journal,35,71;linkingpublicationresults,1:100356,1">On Holyhedra</A>&rdquo;
                   (with an introduction by John Conway),
                   <I>Discrete and Computational Geometry</I>, volume
                   24, number 1, pages 85-104, 2000.
                   There is still work to be done
                   in order to win the $10,000 / (number of faces) reward,
                   because Vinson's polyhedron has 78,585,627 faces and
                   genus 60,380,421!
                   Don Hatch reports
                   <A HREF="http://www.plunk.org/~hatch/Holyhedron/">some
                   further progress</A>: a 492-face holyhedron.
                   <P>
                   John Conway's Angel and Devil Problem has been solved,
                   even for power-2 angel, by
                   <A HREF="http://amathe.dyn.elte.hu/letolt.php?angel-mathe.pdf">Andr&aacute;s M&aacute;th&eacute;</A>
                   and
                   <A HREF="http://home.broadpark.no/~oddvark/angel/Angel.pdf">Oddvar Kloster</A>.
                   See <A HREF="http://sigfpe.blogspot.com/2007/03/angel-problem-has-been-solved-maybe.html">this blog post</A>.
                   There are other solutions, for higher-power angels,
                   by Brian Bowditch and Peter G&aacute;cs.},
  unrefereed    = 1,
}

Abstract:

Open problems from the 15th Annual ACM Symposium on Computational Geometry.

Comments:

This paper is also available as arXiv:cs.CG/9908007 of the Computing Research Repository (CoRR), and from ACM.

Updates:

I understand that Kasturi Varadarajan's problem (is there a topological cube with orthogonal opposite facets?) has been solved by Günter Ziegler.

John Conway's Holyhedron Problem has been solved by Jade Vinson in “On Holyhedra” (with an introduction by John Conway), Discrete and Computational Geometry, volume 24, number 1, pages 85-104, 2000. There is still work to be done in order to win the $10,000 / (number of faces) reward, because Vinson's polyhedron has 78,585,627 faces and genus 60,380,421! Don Hatch reports some further progress: a 492-face holyhedron.

John Conway's Angel and Devil Problem has been solved, even for power-2 angel, by András Máthé and Oddvar Kloster. See this blog post. There are other solutions, for higher-power angels, by Brian Bowditch and Peter Gács.

Length:

The paper is 4 pages.

Availability:

The paper is available in PostScript (112k).

See information on file formats.

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