We study the problem of construction of a convex 3-polytope whose (i) shadow boundary has n vertices and (ii) two hulls, upper and lower, are isomorphic to two given triangulations of a convex n-gon. Barnette [℄ D. W. Barnette. Projections of 3-polytopes. Israel J. Math., 8:304{308, 1970] proved the existence of a convex 3-polytope in general case. We show that, in our case, a polytope can be constructed using an operation of edge creation
This thesis explores two specific topics of discrete geometry, the multitriangulations and the polyt...
AbstractDefine a graph GT(n) with one node for each triangulation of a convex n-gon. Place an edge b...
In this thesis, we present an algorithm for obtaining a triangulation of multiple, non-planar 3D pol...
AbstractGuibas conjectured that given a convex polygon P in the xy-plane along with two triangulatio...
Guibas conjectured that given a convex polygon P in the xy-plane along with two triangulations of i...
AbstractDefine a graph GT(n) with one node for each triangulation of a convex n-gon. Place an edge b...
Steinitz's theorem states that a graph G is the edge-graph of a 3-dimensional convex polyhedron if a...
AbstractA triangulated 3-sphere is said to be polyhedral provided it is isomorphic to the boundary o...
AbstractThe different combinatorial types of triangulations of the 3-sphere with up to 8 vertices ar...
When does a topological polyhedral complex (embedded in Rd) admit a geometric realization (a rectili...
Abstract. We give a new proof of Steinitz’s classical theorem in the case of plane trian-gulations, ...
Let Pn be a convex n-gon in the plane, n ⩾ 3. Consider Σn, the collection of all sets of mutually no...
Steinitz's theorem states that a graph $G$ is the edge-graph of a $3$-dimensional convex polyhedron...
AbstractWe consider convex 3-polytopes with exactly two types of edges. The questions of the existen...
A triangulation of a finite point set A in IR d is a geometric simplicial complex which covers the c...
This thesis explores two specific topics of discrete geometry, the multitriangulations and the polyt...
AbstractDefine a graph GT(n) with one node for each triangulation of a convex n-gon. Place an edge b...
In this thesis, we present an algorithm for obtaining a triangulation of multiple, non-planar 3D pol...
AbstractGuibas conjectured that given a convex polygon P in the xy-plane along with two triangulatio...
Guibas conjectured that given a convex polygon P in the xy-plane along with two triangulations of i...
AbstractDefine a graph GT(n) with one node for each triangulation of a convex n-gon. Place an edge b...
Steinitz's theorem states that a graph G is the edge-graph of a 3-dimensional convex polyhedron if a...
AbstractA triangulated 3-sphere is said to be polyhedral provided it is isomorphic to the boundary o...
AbstractThe different combinatorial types of triangulations of the 3-sphere with up to 8 vertices ar...
When does a topological polyhedral complex (embedded in Rd) admit a geometric realization (a rectili...
Abstract. We give a new proof of Steinitz’s classical theorem in the case of plane trian-gulations, ...
Let Pn be a convex n-gon in the plane, n ⩾ 3. Consider Σn, the collection of all sets of mutually no...
Steinitz's theorem states that a graph $G$ is the edge-graph of a $3$-dimensional convex polyhedron...
AbstractWe consider convex 3-polytopes with exactly two types of edges. The questions of the existen...
A triangulation of a finite point set A in IR d is a geometric simplicial complex which covers the c...
This thesis explores two specific topics of discrete geometry, the multitriangulations and the polyt...
AbstractDefine a graph GT(n) with one node for each triangulation of a convex n-gon. Place an edge b...
In this thesis, we present an algorithm for obtaining a triangulation of multiple, non-planar 3D pol...
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