Square antiprism

In geometry, the square antiprism is the second in an infinite family of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps. It is also known as an anticube. If all its faces are regular, it is a semiregular polyhedron or uniform polyhedron. A nonuniform D4-symmetric variant is the cell of the noble square antiprismatic 72-cell. When eight points are distributed on the surface of a sphere with the aim of maximising the distance between them in some sense, the resulting shape corresponds to a square antiprism rather than a cube. Specific methods of distributing the points include, for example, the Thomson problem (minimizing the sum of all the reciprocals of distances between points), maximising the distance of each point to the nearest point, or minimising the sum of all reciprocals of squares of distances between points. Square antiprismatic molecular geometry According to the VSEPR theory of molecular geometry in chemistry, which is based on the general principle of maximizing the distances between points, a square antiprism is the favoured geometry when eight pairs of electrons surround a central atom. One molecule with this geometry is the octafluoroxenate(VI) ion (XeF82-) in the salt nitrosonium octafluoroxenate(VI); however, the molecule is distorted away from the idealized square antiprism. Very few ions are cubical because such a shape would cause large repulsion between ligands; PaF83- is one of the few examples. In addition, the element sulfur forms octatomic S8 molecules as its most stable allotrope. The S8 molecule has a structure based on the square antiprism, in which the eight atoms occupy the eight vertices of the antiprism, and the eight triangle-triangle edges of the antiprism correspond to single covalent bonds between sulfur atoms. The main building block of the One World Trade Center (at the site of the old World Trade Center destroyed on September 11, 2001) has the shape of an extremely tall tapering square antiprism.

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Truncation (geometry)

In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new facet in place of each vertex. The term originates from Kepler's names for the Archimedean solids. In general any polyhedron (or polytope) can also be truncated with a degree of freedom as to how deep the cut is, as shown in Conway polyhedron notation truncation operation. A special kind of truncation, usually implied, is a uniform truncation, a truncation operator applied to a regular polyhedron (or regular polytope) which creates a resulting uniform polyhedron (uniform polytope) with equal edge lengths.

Skew polygon

In geometry, a skew polygon is a polygon whose vertices are not all coplanar. Skew polygons must have at least four vertices. The interior surface (or area) of such a polygon is not uniquely defined. Skew infinite polygons (apeirogons) have vertices which are not all colinear. A zig-zag skew polygon or antiprismatic polygon has vertices which alternate on two parallel planes, and thus must be even-sided. Regular skew polygons in 3 dimensions (and regular skew apeirogons in two dimensions) are always zig-zag.

Prismatic uniform polyhedron

In geometry, a prismatic uniform polyhedron is a uniform polyhedron with dihedral symmetry. They exist in two infinite families, the uniform prisms and the uniform antiprisms. All have their vertices in parallel planes and are therefore prismatoids. Because they are isogonal (vertex-transitive), their vertex arrangement uniquely corresponds to a symmetry group.

Double bridged mu(2)-Halide Cu (II) complexes for the electrocatalytic reduction of CO2

Kurt Schenk, Farzaneh Fadaei Tirani, Jun Gu

Two dicopper (II) complexes of general formula CuLX2 {L = 2, 5-diphenyl-3, 4(2-pyridyl) cyclopenta-2, 4-dien-1-one, X = Cl (1) or Br (2)} have been synthesized and characterized by elemental analysis, IR, UV-Vis spectroscopic methods. The crystal stru ...

2019

Anionic Bipyridyl Ligands for Applications in Metallasupramolecular Chemistry

Rosario Scopelliti, Kay Severin, Mathieu Jérémie Marmier, Clément Schouwey, Mirela Pascu

The facile synthesis of anionic bipyridyl ligands with dinuclear clathrochelate cores is described. These metalloligands can be obtained in high yields by the reactions of M(ClO4)(2)(H2O)(6) (M: Zn, Mn, or Co) with 4-pyridylboronic acid and 2,6-diformyl-4- ...

Wiley-Blackwell2014

Brilliant Photoluminescence and Triboluminescence from Ternary Complexes of Dy-III and Tb-III with 3-Phenyl-4-propanoy1-5-isoxazolonate and a Bidentate Phosphine Oxide Coligand

Rosario Scopelliti

Three new lanthanide heterocyclic beta-diketonate complexes [Dy(PPI)(3)(EtOH)(2)] (1), [Dy(PPI)(3)(DPEPO)] (2), and [Tb(PPI)(3)(DPEPO)] (3) [where HPPI = 3-pheny1-4-propanoyl-5-isoxazolone and DPEPO = bis(2(diphenylphosphino)phenyl)ether oxide] have been s ...

American Chemical Society2013

Coordination Chemistry: Ligands and Geometries CH-222: Coordination chemistry

Covers coordination numbers, common ligands, and preferred geometries in coordination chemistry, emphasizing the spatial distribution between ligands and the role of d⁸ electron configurations.