Search results for "Plane symmetry"
showing 5 items of 5 documents
Infrared and quantum-chemical studies of the structure and vibrations of methyldisilylamine
2002
Abstract Infrared spectra are reported from labelled species of methyldisilylamine (N(CH 3 )(SiH 3 ) 2 ) in the gas and solid phase. Quantum-chemical (QC) calculations of structure and force field have been carried out at HF, MP2 and B3LYP levels using 6-31G ∗ and 6-311G ∗∗ basis sets. The equilibrium structure belongs to the point group C s with the plane of symmetry at right angles to the NSi 2 angle and a slight non-planarity of the CNSi 2 moiety ( C s ,⊥ ). Spectra in the ν SiH region however suggest an effective C 2 v structure, with two distinct types of SiH bond. Two strong SiH bonds lie in the skeletal plane, eclipsing each other. The single ν is CH band in the CHD 2 species suggest…
The S-kernel: A measure of symmetry of objects
2007
In this paper we introduce a new symmetry feature named ''symmetry kernel'' (SK) to support a measure of symmetry. Given any symmetry transform S, SK of a pattern P is the maximal included symmetric sub-set of P for all directions and shifts. We provide a first algorithm to exhibit this kernel where the centre of symmetry is assumed to be the centre of mass. Then we prove that, in any direction, the optimal axis corresponds to the maximal correlation of a pattern with its symmetric version. That leads to a second algorithm. The associated symmetry measure is a modified difference between the respective surfaces of a pattern and its kernel. A series of experiments supports the actual algorit…
Visual Discrimination of the 17 Plane Symmetry Groups
2011
Within most of the 17 plane symmetry groups, individual symmetry operations act in multiple, nonequivalent ways. This, and the fact that many groups can be realized on the basis of different unit cells and generating regions, poses difficulties for visual discrimination and identification. Because of inherent confounds, only few of the groups can be studied by traditional experimental methodology. The use of an oddity paradigm and specific tiling patterns that camouflage groups in complex textures are recommended as partial remedy to this impasse. In order to prepare readers for an appreciation of the aforementioned issues and to provide a rationale for their investigation, the reporting of…
Copper-, cobalt-, and manganese-containing 17-tungsto-2-germanates.
2009
The sandwich-type tungstogermanates [Cu(3)(H(2)O)(B-beta-GeW(9)O(33)(OH))(B-beta-GeW(8)O(30)(OH))](12-) (1), [Co(H(2)O)(2){Co(3)(B-beta-GeW(9)O(33)(OH))(B-beta-GeW(8)O(30)(OH))}(2)](22-) (2), and [Mn(H(2)O)(2){Mn(3)(H(2)O)(B-beta-GeW(9)O(33)(OH))(B-beta-GeW(8)O(30)(OH))}(2)](22-) (3) were synthesized and characterized by single-crystal X-ray diffraction, elemental analysis, thermogravimetric analysis, and infrared spectroscopy. Polyanion 1 is composed of two nonequivalent Keggin units, (B-beta-GeW(8)O(31)) and (B-beta-GeW(9)O(34)), linked to each other via three copper(II) ions in such a way that there is a plane of symmetry passing through both Ge atoms and the unique Cu atom, resulting in…
Unsupervised learning of category-specific symmetric 3D keypoints from point sets
2020
Lecture Notes in Computer Science, 12370