Related papers: Hybrid spherical designs
The regular polyhedra have the highest order of 3D symmetries and are exceptionally at- tractive templates for (self)-assembly using minimal types of building blocks, from nano-cages and virus capsids to large scale constructions like glass…
We characterize that the image of the embedding of the $Q$-polynomial association scheme into eigenspace by primitive idempotent $E_1$ is a spherical $t$-design in terms of the Krein numbers. And we show that the strengths of $P$- and…
This paper deals with a kind of design of a ruled surface. It combines concepts from the fields of computer aided geometric design and kinematics. A dual unit spherical B\'ezier-like curve on the dual unit sphere (DUS) is obtained with…
We formulate a simple algorithm for computing global exact symmetries of closed discrete curves in plane. The method is based on a suitable trigonometric interpolation of vertices of the given polyline and consequent computation of the…
Graphical designs are an extension of spherical designs to functions on graphs. We connect linear codes to graphical designs on cube graphs, and show that the Hamming code in particular is a highly effective graphical design. We show that…
In this short note we propose a new method for construction new nice arrangement on the sphere $S^d$ using the spaces of spherical harmonic.
It is known that the suspension of a simplicial complex can be realized with only one additional point. Suitable iterations of this construction generate highly symmetric simplicial complexes with various interesting combinatorial and…
We develop the theory of arrangements of spheres. Consider a finite collection of codimension-$1$ subspheres in a positive-dimensional sphere. There are two posets associated with this collection: the poset of faces and the poset of…
We consider the general question of when all orbits under the unitary action of a finite group give a complex spherical design. Those orbits which have large stabilisers are then good candidates for being optimal complex spherical designs.…
A new formula is obtained in algebraic topology, in terms of Betti numbers, and a new method, called the spinal method, is suggested and developed for generating quadrangulations of closed orientable surfaces. Those surfaces arise as the…
In this paper, we present the implicit equations for one special class of real-valued spherical harmonics with octahedral symmetry. Based on this representation, we construct the rotationally invariant measure of deviation from the…
We have identified some necessary conditions for the existence of rigid sphere designs. In particular, we have successfully resolved the conjecture proposed by [Ban87]; Given fixed positive integers t and d, we show that there exist only…
We develop a systematic framework for constructing spherical harmonics on the two-dimensional unit sphere as superpositions of Gaussian beams whose poles form well-separated point configurations. The distributional and analytic properties…
We introduce orthogonal ring patterns in the 2-sphere and in the hyperbolic plane, consisting of pairs of concentric circles, which generalize circle patterns. We show that their radii are described by a discrete integrable system. This is…
We want to introduce a construction of spherical designs from finite graphs with the theory of crystal lattice. We start from a finite graph, and we consider standard realization of the crystal lattices as the maximal Abelian covering of…
This article is devoted to studying complex algebraic sets under (global) blow-spherical equivalence. The main results of this article are complete classifications of complex algebraic curves. Firstly, we present a complete classification…
Skeletal polyhedra and polygonal complexes are finite or infinite periodic structures in 3-space with interesting geometric, combinatorial, and algebraic properties. These structures can be viewed as finite or infinite periodic graphs…
We propose a new method for constructing rational spatial Pythagorean Hodograph (PH) curves based on determining a suitable rational framing motion. While the spherical component of the framing motion is arbitrary, the translation part is…
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and…
A fully implementable filtered polynomial approximation on spherical shells is considered. The method proposed is a quadrature-based version of a filtered polynomial approximation. The radial direction and the angular direction of the…