Honvault, Pascal Euclidean realizations of triangulated polyhedra. (English) £ ¢ ¡ Zbl 07203374 - Archive ouverte HAL Access content directly
Journal Articles Journal for Geometry and Graphics Year : 2019

Honvault, Pascal Euclidean realizations of triangulated polyhedra. (English) £ ¢ ¡ Zbl 07203374

Abstract

The author studies (not necessarily convex) triangulated polyhedra in three-dimensional Euclidean space and with genus zero. The focus of the paper is to devise an algorithm to construct an explicit realization of such a polyhedron given by its combinatorial data: • the number n + 1 and a labelling v 0 , v 1 ,. .. , v n of its vertices • degree sequence (d 0 , d 1 ,. .. , d n), where d i is the number of edges incident to the ith vertex v i • a triangulation given by a list of triangles (v i , v j , v k) The algorithm is guided by a set of necessary and sufficient conditions on the length of the edges, and the internal and external angles of the triangles in the triangulation. Reviewer: Matthias Schymura (Cottbus) MSC: 52B05 Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) 51N20 Euclidean analytic geometry 52-04 Software, source code, etc. for problems pertaining to convex and discrete geometry 51M20 Polyhedra and polytopes; regular figures, division of spaces
No file

Dates and versions

hal-03611658 , version 1 (23-03-2022)

Identifiers

  • HAL Id : hal-03611658 , version 1

Cite

Pascal Honvault. Honvault, Pascal Euclidean realizations of triangulated polyhedra. (English) £ ¢ ¡ Zbl 07203374. Journal for Geometry and Graphics, 2019, 23 (2), pp.157-165. ⟨hal-03611658⟩
19 View
1 Download

Share

Gmail Facebook X LinkedIn More