Geodesic
The generalized Reye configuration
Ars Mathematica Contemporanea, Tome 3 (2010) no. 1, pp. 21-27.

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Given an embedding in the plane of the vertices of a cube, we consider conditions on the embedded vertices such that they are the projection of the vertices of a 3 dimensional polyhedron combinatorially equivalent to the cube. We are particularly interested in conditions expressible as incidence conditions for the lines induced by the given vertex set in the plane. We show that the vertices and their incidences extend to a Reye configuration in the plane if and only if the vertices are the projection of a parallelepiped. More generally, the positions of the embedded vertices result from projecting a polyhedron combinatorially equivalent to the cube if and only if they belong to a plane configuration we call the generalized Reye configuration.
DOI : 10.26493/1855-3974.108.423
Keywords: configuration 
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Brigitte Servatius; Herman Servatius. The generalized Reye configuration. Ars Mathematica Contemporanea, Tome 3 (2010) no. 1, pp. 21-27. doi : 10.26493/1855-3974.108.423. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.108.423/

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