How to cage an egg

• Published in 1992
• Added on 2026-03-14

This paper proves that given a convex polyhedron \(P \subset \mathbb{R}^3\) and a smooth strictly convex body \(K \subset \mathbb{R}^3\), there is some convex polyhedron \(Q\) combinatorically equivalent to \(P\) which midscribes \(K\); that is, all the edges of \(Q\) are tangent to \(K\). Furthermore, with some stronger smoothnesss conditions on \(\partial K\), the space of all such \(Q\) is a six dimensional differentiable manifold.

Links

• https://eudml.org/doc/143977
• https://gdz.sub.uni-goettingen.de/id/PPN356556735_0107

Other information

BibTeX entry

@article{Howtocageanegg,
	key = {Howtocageanegg},
	type = {article},
	title = {How to cage an egg},
	author = {Oded Schramm},
	abstract = {This paper proves that given a convex polyhedron \(P \subset \mathbb{\{}R{\}}^3\) and a smooth strictly convex body \(K \subset \mathbb{\{}R{\}}^3\), there is some convex polyhedron \(Q\) combinatorically equivalent to \(P\) which midscribes \(K\); that is, all the edges of \(Q\) are tangent to \(K\). Furthermore, with some stronger smoothnesss conditions on \(\partial K\), the space of all such \(Q\) is a six dimensional differentiable manifold.},
	comment = {},
	date_added = {2026-03-14},
	date_published = {1992-03-14},
	urls = {https://eudml.org/doc/143977,https://gdz.sub.uni-goettingen.de/id/PPN356556735{\_}0107},
	collections = {attention-grabbing-titles,food,fun-maths-facts,geometry},
	url = {https://eudml.org/doc/143977 https://gdz.sub.uni-goettingen.de/id/PPN356556735{\_}0107},
	urldate = {2026-03-14},
	year = 1992,
	journal = {Inventiones mathematicae},
	volume = 107,
	issue = 3,
	issn = {0020-9910; 1432-1297/e},
	identifier = {urn:eudml:doc:143977},
	pages = {543-560}
}