相关论文: Polar Zonohedra Edge-Unfold to Nets

Polypolyhedra are edge-transitive compounds of polyhedra. In this paper we use group theory to determine the number of distinct polypolyhedra whose symmetry group is any given finite irreducible Coxeter group. We apply this result in order…

We prove that every tetrahedron T has a simple, closed quasigeodesic that passes through three vertices of T. Equivalently, every T has a face whose "exterior angles" are at most pi.

We demonstrate that single scattering of p-polarized waves from uncorrelated surface and volume disorder can lead to perfect depolarization. The degree of polarization is shown to vanish in specific scattering directions that can be…

We introduce a model system of anisotropic colloidal `rocks'. Due to their shape, the bonding introduced via non-absorbing polymers is profoundly different from spherical particles: bonds between rocks are rigid against rotation, leading to…

In this paper, we prove a dihedral extremality and rigidity theorem for a large class of codimension zero submanifolds with polyhedral boundary in warped product manifolds. We remark that the spaces considered in this paper are not…

In every Engel manifold we construct an infinite family of pairwise non-isotopic transverse tori that are all smoothly isotopic. To distinguish the transverse tori in the family we introduce a homological invariant of transverse tori that…

We prove that any polyhedron of genus zero or genus one built out of rectangular faces must be an orthogonal polyhedron, but that there are nonorthogonal polyhedra of genus seven all of whose faces are rectangles. This leads to a resolution…

We construct the first two continuous bloomings of all convex polyhedra. First, the source unfolding can be continuously bloomed. Second, any unfolding of a convex polyhedron can be refined (further cut, by a linear number of cuts) to have…

We introduce a model of polarization in networks as a unifying framework for the measurement of polarization that covers a wide range of applications. We consider a sufficiently general setup for this purpose: node- and edge-weighted,…

We report polarization tomography experiments on metallic nanohole arrays with square and hexagonal symmetry. As a main result, we find that a fully polarized input beam is partly depolarized after transmission through a nanohole array.…

We survey literature on all known families and examples of Dehn invariant zero tetrahedra. We also contribute two previously unknown families of Dehn invariant zero tetrahedra. Following a suggestion of Dill and Habegger, we show that there…

This paper is a study of the interaction between the combinatorics of boundaries of convex polytopes in arbitrary dimension and their metric geometry. Let S be the boundary of a convex polytope of dimension d+1, or more generally let S be a…

We completely classify edge-to-edge tilings of the sphere by congruent quadrilaterals. As part of the classification, we also present a modern version of the classification of edge-to-edge tilings of the sphere by congruent triangles.…

Let C be a simple, closed, directed curve on the surface of a convex polyhedron P. We identify several classes of curves C that "live on a cone," in the sense that C and a neighborhood to one side may be isometrically embedded on the…

The Erd\H{o}s-Anning theorem states that every point set in the Euclidean plane with integer distances must be either collinear or finite. More strongly, for any (non-degenerate) triangle of diameter~$\delta$, at most $O(\delta^2)$ points…

We give a short, topological proof that all graphs admit tree-decompositions displaying their topological ends.

We show, in this note, that on any symplectic supermanifold, even or odd, there exist an infinite dimensional affine space of symmetric connections, compatible to the symplectic form.

This is an example on the cohomology of threefolds.

Zonotopes are studied from the point of view of central symmetry and how volumes of facets and the angles between them determine a zonotope uniquely. New proofs are given for theorems of Shephard and McMullen characterizing a zonotope by…

A group action is called polar if there exists an immersed submanifold (a section) which intersects all orbits orthogonally. Such group actions have been studied extensively on symmetric spaces. We show how to construct a manifold admitting…