AbstractIn a recent paper, Karpenkov has classified the lattice polytopes (that is, with vertices in the integer lattice Zd) which are regular with respect to those affinities which preserve the lattice. An alternative approach is adopted in this paper. For each regular polytope P in euclidean space Ed, those lattices Λ are classified which are compatible with P, in the sense that some translate of Λ contains the vertices of P, and this translate is preserved by the symmetries of P
AbstractThe question of when one regular polytope (finite, convex) embedds in the vertices of anothe...
We enumerate the regular and chiral polyhedra (in the sense of Grünbaum’s skeletal approach) whose v...
We enumerate the regular and chiral polyhedra (in the sense of Grünbaum’s skeletal approach) whose v...
We completely describe lattice convex polytopes in ℝ n (for any dimension n) that are regular with r...
AbstractWe say that a (d+1)-polytope P is an extension of a polytope K if the facets or the vertex f...
It is shown here that every L-polytope of an even unimodular lattice does not generate the lattice. ...
Abstract. A polyhedral norm is a norm N on Rn for which the set N(x) ≤ 1 is a polytope. This covers...
Regularity has often been present in the form of regular polyhedra or tessellations; classical examp...
In this paper, we explore the structure of the set of all regular equivalences (White and Reitz 1983...
AbstractWe show that any smooth Q-normal lattice polytope P of dimension n and degree d is a strict ...
In 1980, Arnold studied the classification problem for convex lattice polygons of given area. Since ...
AbstractVoronoi defines a partition of the cone of positive semidefinite n -ary formsPn into L -type...
AbstractWe introduce the property of convex normality of rational polytopes and give a dimensionally...
AbstractIn this paper it is shown that all regular polytopes are Ramsey. In the course of this proof...
We show that any finite affinely independent set can be isometrically embedded into a regular polygo...
AbstractThe question of when one regular polytope (finite, convex) embedds in the vertices of anothe...
We enumerate the regular and chiral polyhedra (in the sense of Grünbaum’s skeletal approach) whose v...
We enumerate the regular and chiral polyhedra (in the sense of Grünbaum’s skeletal approach) whose v...
We completely describe lattice convex polytopes in ℝ n (for any dimension n) that are regular with r...
AbstractWe say that a (d+1)-polytope P is an extension of a polytope K if the facets or the vertex f...
It is shown here that every L-polytope of an even unimodular lattice does not generate the lattice. ...
Abstract. A polyhedral norm is a norm N on Rn for which the set N(x) ≤ 1 is a polytope. This covers...
Regularity has often been present in the form of regular polyhedra or tessellations; classical examp...
In this paper, we explore the structure of the set of all regular equivalences (White and Reitz 1983...
AbstractWe show that any smooth Q-normal lattice polytope P of dimension n and degree d is a strict ...
In 1980, Arnold studied the classification problem for convex lattice polygons of given area. Since ...
AbstractVoronoi defines a partition of the cone of positive semidefinite n -ary formsPn into L -type...
AbstractWe introduce the property of convex normality of rational polytopes and give a dimensionally...
AbstractIn this paper it is shown that all regular polytopes are Ramsey. In the course of this proof...
We show that any finite affinely independent set can be isometrically embedded into a regular polygo...
AbstractThe question of when one regular polytope (finite, convex) embedds in the vertices of anothe...
We enumerate the regular and chiral polyhedra (in the sense of Grünbaum’s skeletal approach) whose v...
We enumerate the regular and chiral polyhedra (in the sense of Grünbaum’s skeletal approach) whose v...
DOI
Add to ORKG