Last Update 20/ 05/ 2000

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The three fold axis in the cube is studied by an interactive rotation of its projection under mouse action on the figure. This way, when the cube projection is rotated around one of its six binary symmetry axes placed on this screen's plane it enables successive orientation of four of its thirteen symmetry axes perpendicular to the mentioned binary axis. The binary axis can be rotated displacing the Vertical Scrolling Bar (VSB) to reach any of the angles given on the table below, the second axis can be activated displacing the Horizontal Scrolling Bar (HSB) on the figure, as can be observed in the table below.

Table: VSB angle to get the orientation of the respective axis in the HSB
  VSB=0o VSB=55o VSB=90o VSB=125o
Axis HSB C4 C3 C2 C3

When HSB activates the four fold axis (C4) only four corners of the cube will be visible, when C3 only seven corners visible and when C2 will be activated only six corners will be visible, the other corners will stay eclipsed. Other pages on symmetry axis can be consulted on the table of chemistry subjects on the bottom of this page.

The little structures at the right side of the figure can modify the cube, just pointing the cursor and click to select. Push and drag the mouse in the inner part of the cube to observe combined rotation.

Suggested activity

For each proposed structure, find the symmetry elements. Admit the blue sphere and the red sphere as different objects.

Please send your comments.

Table of subjects.
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
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
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
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
Electrochemical cell
Ethane conformations
Oxidation and reduction
Resources of chemical-ICT: water, health and symmetry
Solid and liquid gold