In previous work we showed that the only finite nonabelian simple group acting by diffeomorphisms on a homology 3sphere is the alternating or dodecahedral group A5. Here we characterize finite nonsolvable groups that act on a homology 3-sphere preserving orientation. We find exactly the finite nonsolvable groups that act orthogonally on the 3-sphere, plus two families of groups for which we do ...

Observational data hint at a finite universe, with spherical manifolds such as the Poincaré dodecahedral space tentatively providing the best fit. Simulating the physics of a model universe requires knowing the eigenmodes of the Laplace operator on the space. The present article provides explicit polynomial eigenmodes for all globally homogeneous 3-manifolds: the Poincaré dodecahedral space S3/...

A discrete Fourier analysis on the dodecahedron is studied, from which results on a tetrahedron is deduced by invariance. The results include Fourier analysis in trigonometric functions, interpolation and cubature formulas on these domains. In particular, a trigonometric Lagrange interpolation on the tetrahedron is shown to satisfy an explicit compact formula and the Lebesgue constant of the in...

We study the critical behavior of discrete spin models related to the 2d O(3) non-linear sigma model. Precise numerical results suggest that models with sufficiently large discrete subgroups are in the same universality class as the original sigma model. We observe that at least up to correlation lengths ξ ≈ 300 the cut-off effects follow effectively an ∝ a behaviour both in the O(3) and in the...

Nanomaterials with particular nanostructures which usually possess special properties always attract considerable attention. A novel bimetallic Pt/Cu hexapod nanostructure was prepared by a facile one-pot strategy. The formation mechanism was investigated by the time sequential evolution experiments and the hexapod concave nanostructures originated from the Pt/Cu rhombic dodecahedron. Further e...

Colloidal self-assembly has enormous potential as a bottom-up means of structure fabrication. Here we demonstrate hierarchical self-assembly of rationally designed charge-stabilised colloidal magnetic particles into ground state structures that are topologically equivalent to a snub cube and a snub dodecahedron, the only two chiral Archimedean solids, for size-selected clusters. These spherical...

Immersive Media’s Telemmersion® system is a multi-view imaging system that captures high-resolution full-motion 360o omni-directional images from synchronized cameras arranged in a dodecahedron. This paper describes transformation of the resultant imagery from aesthetically pleasing blended mosaics to mathematically rigorous projections through camera calibration. Specifically, we describe our ...

Purified preparations of echovirus 22 were examined in the electron microscope. The virus was found to possess 32 capsomers arranged at the vertices of either a pentakis dodecahedron or a rhombic triacontahedron. The size of the virions ranges from 22 x 10(-3) to 32 x 10(-3) mum with a mean of 27 x 10(-3) mum and a mode of 28 x 10(-3) mum.

New strange fulleroids are built up by using the three classical composite map operations: tripling (leapfrog Le), quadrupling (chamfering Q) and septupling (capra Ca) on the starting structure dodecahedron. These transforms belong to the icosahedral symmetry group and show interesting mathematical and (possible) physico-chemical properties. Topological symmetry data of the presented cages are ...