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Joseph O'Rourke
Joseph O'Rourke
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You may be interested in this negative result, thatwhich shows the space of realizations of an abstract $4$-polytope may be arbitrarily wild:

![Universality4Polytopes][1]
Quote from the [*Handbook of Discrete and Computational Geometry*](http://www.crcpress.com/product/isbn/9781584883012), 2nd Edition, p.370.

As the link Hugh Thomas provided indicates, Richter-Gebert also proved that determining whether an abstract polytope is realizable is NP-hard for fixed dimensions $d \ge 4$.

You may be interested in this negative result, that shows the space of realizations of an abstract $4$-polytope may be arbitrarily wild:

![Universality4Polytopes][1]
Quote from the [*Handbook of Discrete and Computational Geometry*](http://www.crcpress.com/product/isbn/9781584883012), 2nd Edition, p.370.

You may be interested in this negative result, which shows the space of realizations of an abstract $4$-polytope may be arbitrarily wild:

![Universality4Polytopes][1]
Quote from the [*Handbook of Discrete and Computational Geometry*](http://www.crcpress.com/product/isbn/9781584883012), 2nd Edition, p.370.

As the link Hugh Thomas provided indicates, Richter-Gebert also proved that determining whether an abstract polytope is realizable is NP-hard for fixed dimensions $d \ge 4$.

Source Link
Joseph O'Rourke
Joseph O'Rourke
  • 150.9k
  • 36
  • 358
  • 958

You may be interested in this negative result, that shows the space of realizations of an abstract $4$-polytope may be arbitrarily wild:

![Universality4Polytopes][1]
Quote from the [*Handbook of Discrete and Computational Geometry*](http://www.crcpress.com/product/isbn/9781584883012), 2nd Edition, p.370.