With the development of computer graphics and virtual realities, the demand for a content-based 3D model retrieval system becomes urgent. In this study, two features, grid sphere and dodecahedral silhouettes, are proposed and combined for 3D model retrieval. The experiments are conducted on a 3D model database. Experiment results show that the proposed methods are superior to others.

In 3-dimensional Euclidean space there exist two exceptional polyhedra, the rhombic dodecahedron and triacontahedron, only known polytopes (besides polygons) that are edge-transitive without being vertex-transitive. We show these polyhedra do not have higher-dimensional analogues, is, in dimension d ? 4, edge-transitivity of convex implies vertex-transitivity.More generally, we give a classific...

We present a construction of highly entangled states defined on the topology platonic solid using tensor networks based ancillary Absolute Maximally Entangled (AME) states. illustrate idea example quantum state AME(5,2) over dodecahedron. analyze entropy such many different partitions, and observe that they come integer numbers are almost maximal. also all solids accept AME Reed-Solomon codes s...

We prove that an irreducible 3-manifold whose fundamental group satisfies a certain group-theoretic property called RFRS is virtually fibered. As a corollary, we show that 3-dimensional reflection orbifolds and arithmetic hyperbolic orbifolds defined by a quadratic form virtually fiber. These include the Seifert Weber dodecahedral space and the Bianchi groups. Moreover, we show that a taut sutu...

The splitting method was defined by the author in [Margenstern 2002a, Margenstern 2002d]. It is at the basis of the notion of combinatoric tilings. As a consequence of this notion, there is a recurrence sequence which allows us to compute the number of tiles which are at a fixed distance from a given tile. A polynomial is attached to the sequence as well as a language which can be used for impl...

In this paper we survey most of the recent and often surprising results on packings of congruent spheres in d-dimensional spaces of constant curvature. The topics discussed are as follows: Hadwiger numbers of convex bodies and kissing numbers of spheres; Touching numbers of convex bodies; Newton numbers of convex bodies; One-sided Hadwiger and kissing numbers; Contact graphs of finite packings ...

Geometry constrains but does not dictate the topology of the three-dimensional space. In a locally spatially homogeneous and isotropic universe, however, the topology of its spatial section dictates its geometry. We show that, besides determining the geometry, the knowledge of the spatial topology through the circles-in-the-sky offers an effective way of setting constraints on the density param...

In this paper, the elastic field in an infinite elastic body containing a polyhedral inclusion with uniform eigenstrains is investigated. Exact solutions are obtained for the stress field in and around a fully general polyhedron, i.e., an arbitrary bounded region of threedimensional space with a piecewise planner boundary. Numerical results are presented for the stress field and the strain ener...

The H-force number of a hamiltonian graph G is the smallest number k with the property that there exists a set W ⊆ V (G) with |W | = k such that each cycle passing through all vertices of W is a hamiltonian cycle. In this paper, we determine the H-force numbers of generalized dodecahedra.

It is proved that the projection constants of twoand three-dimensional spaces are bounded by 4/3 and (1 + √ 5)/2, respectively. These bounds are attained precisely by the spaces whose unit balls are the regular hexagon and dodecahedron. In fact, a general inequality for the projection constant of a real or complex n-dimensional space is obtained and the question of equality therein is discussed...