## Ares Ribó Mor, Günter Rote, and André Schulz:

# 1. Embedding 3-polytopes on a small grid

*In: Proceedings of the 23rd Annual Symposium on Computational
Geometry, Gyeongju, South Korea, June 6–8, 2007*. Association for
Computing Machinery, 2007, pp. 112–118. doi:10.1145/1247069.1247086
# 2. Small grid embeddings of 3-polytopes

*Discrete and Computational
Geometry* **45** (2011), 65–87. doi:10.1007/s00454-010-9301-0,
arXiv:0908.0488 [cs.CG].
### Abstract

We present a constructive method for embedding a 3-connected planar graph with
` n` vertices as a 3-polytope with small integer coordinates. The
embedding will need no coordinate greater than
`O`(2^{7.55n})=`O`(188^{n}).
Finding a plane embedding which supports an equilibrium stress is the crucial
part in the construction. In order to guarantee that the size of the
coordinates and the stresses are small, we extend Tutte's spring embedding
method.

Last update: August 15, 2017.