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Valence shell electron pair repulsion (VSEPR) theory (/ ˈ v ɛ s p ər, v ə ˈ s ɛ p ər / VESP-ər, [1]: 410 və-SEP-ər [2]) is a model used in chemistry to predict the geometry of individual molecules from the number of electron pairs surrounding their central atoms. [3]
In three-dimensional symmetry point groups, the transformations preserving a polyhedron's symmetry include the rotation around the line passing through the base center, known as the axis of symmetry, and the reflection relative to perpendicular planes passing through the bisector of a base, which is known as the pyramidal symmetry of order .
Major types of shapes that either constitute or define a volume. Figure Definitions Images Parallelepiped: A polyhedron with six faces , each of which is a parallelogram; A hexahedron with three pairs of parallel faces; A prism of which the base is a parallelogram; Rhombohedron: A parallelepiped where all edges are the same length
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 (XeF 2−
In three-dimensional space, its most symmetric form is generated from six line segments parallel to the face diagonals of a cube. [2] It tiles space to form the bitruncated cubic honeycomb . Any zonohedron whose faces have the same combinatorial structure as one of these five shapes is a parallelohedron, regardless of its particular angles or ...
This means that a triangular prism has regular faces and has an isogonal symmetry on vertices. [6] The three-dimensional symmetry group of a right triangular prism is dihedral group D 3 h of order 12: the appearance is unchanged if the triangular prism is rotated one- and two- thirds of a full angle around its axis of symmetry passing through ...
The parallelepiped with D 4h symmetry is known as a square cuboid, which has two square faces and four congruent rectangular faces. The parallelepiped with D 3d symmetry is known as a trigonal trapezohedron , which has six congruent rhombic faces (also called an isohedral rhombohedron ).
An icosahedron and related symmetry polyhedra can be used to define a high geodesic polyhedron by dividing triangular faces into smaller triangles, and projecting all the new vertices onto a sphere. Higher order polygonal faces can be divided into triangles by adding new vertices centered on each face.