# Conditions nécessaires et suffisantes pour l’équivalence des polyèdres de l’espace euclidien à trois dimensions

@article{Sydler1965ConditionsNE, title={Conditions n{\'e}cessaires et suffisantes pour l’{\'e}quivalence des poly{\`e}dres de l’espace euclidien {\`a} trois dimensions}, author={J. P. Sydler}, journal={Commentarii Mathematici Helvetici}, year={1965}, volume={40}, pages={43-80} }

## 66 Citations

Hinged Dissections Exist

- Mathematics, Computer ScienceSCG '08
- 2008

It is proved that any finite collection of polygons of equal area has a common hinged dissection, which generalizes and indeed builds upon the result from 1814 that polygons have common dissections (without hinges).

Constant Weight Codes: A Geometric Approach Based on Dissections

- Computer Science
- 2007

A novel geometric method is proposed in which information and code vectors are represented by vectors in w- dimensional Euclidean space, and a one-to-one mapping is established by dissecting the covering polytopes in a specific manner, thereby ensuring unique decodability.

Polytopes that Fill Rn and Scissors Congruence

- MathematicsDiscret. Comput. Geom.
- 1995

In dimensions up to 4, any such polytope P is Euclidean scissors congruent to an n-cube.

Equidecomposability of Polyhedra: A Solution of Hilbert’s Third Problem in Kraków before ICM 1900

- MathematicsThe Mathematical Intelligencer
- 2018

D uring the International Congress of Mathematicians in Paris in 1900, David Hilbert gave a talk on the problems that, in his opinion, would influence mathematics in the 20th century. Later, in the…

Orthogonal dissection into few rectangles

- Computer ScienceArXiv
- 2022

We describe a polynomial time algorithm that takes as input a polygon with axis-parallel sides but irrational vertex coordinates, and outputs a set of as few rectangles as possible into which it can…

Green computing: three examples of how non-trivial mathematical analysis can help

- Computer ScienceJournal of Smart Environments and Green Computing
- 2021

In this paper, three examples are provided that show that in all three directions, non-trivial mathematical analysis can help in environment-related computing research.

Geometry and Topology

- MathematicsLandscape of 21st Century Mathematics
- 2021

This chapter presents a collection of theorems in geometry and topology, proved in the twenty-first, which are at the same time great and easy to understand. The chapter is written for undergraduate…

The strong Suslin reciprocity law

- MathematicsCompositio Mathematica
- 2021

We prove the strong Suslin reciprocity law conjectured by A. Goncharov. The Suslin reciprocity law is a generalization of the Weil reciprocity law to higher Milnor $K$-theory. The Milnor $K$-groups…

PRESS RELEASE: TETRAHEDRA WITH RATIONAL DIHEDRAL ANGLES

- Mathematics
- 2020

(1) Given a tetrahedron, does it tile space? That is, can one fill space with copies of the tetrahedron? Aristotle claimed that one could tile space with copies of a regular tetrahedron, but 1800…

## References

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Sur la décomposition des polyèdres

- Mathematics
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