Add to ORKGWe show that the hypercube has a face-unfolding that tiles space, and that unfolding has an edge-unfolding that tiles the plane. So the hypercube is a dimension-descending tiler. We also show that the hypercube cross unfolding made famous by Dali tiles space, but we leave open the question of whether or not it has an edge-unfolding that tiles the plane
Unfolding a convex polyhedron into a simple planar polygon is a well-studied problem. In this paper,...
The problem of tiling or tessellating (i.e., completely filling) three-dimensional Euclidean space R...
AbstractWe give a structural description of cube tilings and unextendible cube packings of R3. We al...
An unfolding of a polyhedron is a cutting along its surface such that the surface remains connected ...
This article presents a method for unraveling the hypercube and obtaining the 3D-cross (tesseract) t...
We define a notion for unfolding smooth, ruled surfaces, and prove that every smooth prismatoid (the...
International audienceIn this article, we suggest a grid-unfolding of level 1 Menger polycubes of ar...
It is unknown whether every polycube (polyhedron constructed by gluing cubes face-to-face) has an ed...
International audienceWe construct a class of polycubes that tile the space by translation in a latt...
In this article we introduce a new type of Pascal pyramids. A regular squared mosaic in the hyperbol...
More than eighty years ago, Erdos considered sums of the side lengths of squares packed into a unit ...
An unfolding of a polyhedron is produced by cutting the surface and flattening to a single, connecte...
Surface visualization is very important within scientific visualization. The surfaces depict a value...
For any dimension n ≥ 3, we establish the corner poset, a natural triangular poset structure on the ...
We construct a sequence of convex polyhedra on n vertices with the property that, as n -\u3e infinit...
Unfolding a convex polyhedron into a simple planar polygon is a well-studied problem. In this paper,...
The problem of tiling or tessellating (i.e., completely filling) three-dimensional Euclidean space R...
AbstractWe give a structural description of cube tilings and unextendible cube packings of R3. We al...
An unfolding of a polyhedron is a cutting along its surface such that the surface remains connected ...
This article presents a method for unraveling the hypercube and obtaining the 3D-cross (tesseract) t...
We define a notion for unfolding smooth, ruled surfaces, and prove that every smooth prismatoid (the...
International audienceIn this article, we suggest a grid-unfolding of level 1 Menger polycubes of ar...
It is unknown whether every polycube (polyhedron constructed by gluing cubes face-to-face) has an ed...
International audienceWe construct a class of polycubes that tile the space by translation in a latt...
In this article we introduce a new type of Pascal pyramids. A regular squared mosaic in the hyperbol...
More than eighty years ago, Erdos considered sums of the side lengths of squares packed into a unit ...
An unfolding of a polyhedron is produced by cutting the surface and flattening to a single, connecte...
Surface visualization is very important within scientific visualization. The surfaces depict a value...
For any dimension n ≥ 3, we establish the corner poset, a natural triangular poset structure on the ...
We construct a sequence of convex polyhedra on n vertices with the property that, as n -\u3e infinit...
Unfolding a convex polyhedron into a simple planar polygon is a well-studied problem. In this paper,...
The problem of tiling or tessellating (i.e., completely filling) three-dimensional Euclidean space R...
AbstractWe give a structural description of cube tilings and unextendible cube packings of R3. We al...