2001Oxford University Press eBooksRequires access

Symmetry elements, symmetry operations and point groups

Ogden J.S

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Abstract

This chapter describes symmetrical shapes in terms of a plane or line of symmetry and axis of symmetry, which are considered the most identifiable ones exhibited by the majority of symmetrical molecular species. It clarifies that a shape possesses a plane of symmetry if the operation of reflection in the plane results in an equivalent mirror image. It also examines how a shape possesses an axis of symmetry when simple rotation about such an axis leads to an equivalent configuration. The chapter specifies the location of a plane within a molecule and covers various subscripts that identify the position of the plane either in relation to other symmetry elements or to an established coordinate system. It discusses the rotation-reflection axis, which represent the rotational equivalence exhibited by some shapes.

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What this paper is about

This chapter describes symmetrical shapes in terms of a plane or line of symmetry and axis of symmetry, which are considered the most identifiable ones exhibited by the majority of symmetrical molecular species. It clarifies that a shape possesses a plane of symmetry if the operation of reflection in the plane results in an equivalent mirror image. It also examines how a shape possesses an axis of symmetry when simple rotation about such an axis leads to an equivalent configuration. The chapter specifies the location of a plane within a molecule and covers various subscripts that identify the position of the plane either in relation to other symmetry elements or to an established coordinate system. It discusses the rotation-reflection axis, which represent the rotational equivalence exhibited by some shapes.

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Available abstract

This chapter describes symmetrical shapes in terms of a plane or line of symmetry and axis of symmetry, which are considered the most identifiable ones exhibited by the majority of symmetrical molecular species. It clarifies that a shape possesses a plane of symmetry if the operation of reflection in the plane results in an equivalent mirror image. It also examines how a shape possesses an axis of symmetry when simple rotation about such an axis leads to an equivalent configuration. The chapter specifies the location of a plane within a molecule and covers various subscripts that identify the position of the plane either in relation to other symmetry elements or to an established coordinate system. It discusses the rotation-reflection axis, which represent the rotational equivalence exhibited by some shapes.

Key concepts: Plane symmetry, Reflection symmetry, Rotational symmetry, Symmetry (geometry), Symmetry operation, Rotation (mathematics), Plane (geometry), Physics

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