c2mm

Last Update 04/ 3/ 2013

in English/ in Portuguese

Here one of more than 30 examples of two dimensional objects periodically repeated in space according to the rectangular centered group c2mm can be observed every time this page is uploaded. Each straight line segment in red represents a mirror plane, but binary axes and glide planes given in the reference below are not represented in this page. It means that those symmetry elements are still operating and can be detected, as suggested by exercises 1-4. Interaction succeeds a click on any gray rectangle.
Letter "M" is the label for multiplicity, letters "P.s." mean point symmetry and "S.o." for symmetry operations.
When the mouse pointer is moved close to the rectangular cell, the pointer's coordinates are displayed in the status bar displayed in the browser.
The periodic structure of the plane group c2mm will exhibit at least one object characterized by any of the point groups: 1, m, 2, and 2mm. When at least one object exists at position 1 it will be classified as in a general position. Any object in any of the positions m, 2, and 2mm will be classified as in a special position.
Differently from objects in group p2mm, here in group c2mm all the environment on the origin will be repeated on the center of the rectangular cell. For this reason objects in comparable positions in cell p2mm will have here twice the multiplicity of the former.

Exercises

1) Write the coordinates of the center of a disk  in general position in a copy of a selected example, close to the cell origin and write the coordinates of the next disk center obtained after:

1a] a reflection by a glide plane with Miller indices (4 0).

1b] a reflection by a mirror plane with Miller indices (0 2).

1c] a rotation about a binary axis at coordinates x = 0.25 and y = 0.25.

2) Apply the operations given in 1a], 1b], and 1c] for the coordinates of a disk in special position in a copy of one of the examples of this page. Write the significant differences and similarities observed.

5) Why it does not exist any location for an object with multiplicity M = 1 in the group c2mm ?

Reference

International Tables for Crystallography (2005). Vol. A, edited by T. Hahn, Dordrecht: Springer.

Please send your comments.

Table of subjects.
Presentation
Chemistry Analytical Chromatography
Elemental organic analysis
Volumetric analysis, simulation
Crystallography 3 fold screw axis
4 fold inversion axis on tetrahedron
5 fold rotation axis absent in crystallography
c2mm
Binary axis and reflection plane in stereographic projection
Bravais lattices
Conic sections under symmetry operators
Converting from spherical coordinates to stereographic projection
Crystal lattice and unit cell
Determination of unit cell
Elements of symmetry in action - animation
Elements of symmetry in action - cube game
Elements of symmetry in action - dodecahedron game
Elements of symmetry in action - icosahedron game
Elements of symmetry in action - octahedron game
Elements of symmetry in action - tetrahedron game
Ewald sphere and crystal measurements
Extinctions
Five classes in the cubic system
Five classes in the rhombohedral system
From tetrahedron to prism
Gnomonic projection
Improper symmetry axis
Miller indices
Miller indices - animation
Miller indices - cube game
Miller indices - octahedron game
Miller indices - rhombic dodecahedron game
Miller indices - tetrahedron game
Mirror plane
Mirror planes and Miller indices game - tetrahedron
Orientations of the cube
p2mm
Plane symmetry groups
Question on point group
Rotation axis in octahedron and Werner compounds
Rotation axis on tetrahedron and organic molecules
Rotation of objects about an arbitrary axis
Rotation of the parallel and stereographic projections of the cube
Rotation of the stereographic and parallel projection of the cube III
Seven faces in stereographic projection
Seven classes in the hexagonal system
Seven classes in the tetragonal system
Six elements of symmetry in seven orientations
Spherical projection of the octahedron
Stereographic projection
Stereographic projection of six polyhedra in different orientations
Straight line equations and symmetry elements
Symmetry, 2 fold axis
Symmetry, 2, 3 and 6 fold axis in benzene
Symmetry, 3 fold axis in the cube
Symmetry, 4 fold axis in the cube
Symmetry, 4 fold axis in the unit cell of gold
Symmetry elements and Miller indices game
Symmetry elements and Miller indices game - octahedron
Symmetry in art and in crystallography
Three classes in the monoclinic system
Three classes in the orthorhombic system
Twin crystals
Two classes in the triclinic system
Unit cell in hexagonal net
General Butane conformations
Density
Electrochemical cell
Ethane conformations
Oxidation and reduction
Resources of chemical-ICT: water, health and symmetry
Solid and liquid gold