What's special about the point group 432?

In summary, the point group 432 is a symmetry group in three dimensions, denoted by the symbol O, that has 24 elements including rotations and reflections. It is special because it has the highest degree of symmetry for an object in three dimensions and is used in science to classify and study the symmetry of molecules and crystals. An example of an object with point group 432 symmetry is a regular octahedron. It is a subgroup of the larger symmetry group O(3) and is related to other point groups with lower degrees of symmetry.
  • #1
johng23
294
1
Every non-centrosymmetric point group is piezoelectric, except 432. It is neither centrosymmetric nor piezoelectric. Why?
 
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  • #2
Well I guess there isn't really an intuitive reason for this, you just have to do the calculation. If anyone is interested, you can look in Nye's "Physical Properties of Crystals". It turns out that the 4-fold axis leaves 7 of the piezoelectric coefficients nonzero, and the 3 fold axis destroys all of these. 432 is the only group with both a 4 fold and a 3 fold axis.
 
  • #3
well,as for 432, it has a much high symmetric, so all the vector of its charecterastics must be zero
 

Related to What's special about the point group 432?

1. What is the point group 432?

The point group 432 is a symmetry group in three dimensions, also known as the octahedral group. It has 24 elements, including rotations and reflections, and is denoted by the symbol O.

2. What makes the point group 432 special?

The point group 432 is special because it has the highest degree of symmetry for an object in three dimensions. It includes all possible rotations and reflections that can be applied to an object without changing its appearance.

3. How is the point group 432 used in science?

The point group 432 is used in science to classify and study the symmetry of molecules and crystals. It helps scientists understand the physical and chemical properties of these structures and how they interact with other substances.

4. Can you give an example of an object with point group 432 symmetry?

An example of an object with point group 432 symmetry is a regular octahedron, which has eight triangular faces and six vertices. This shape can be rotated and reflected in 24 different ways without changing its appearance.

5. How is the point group 432 related to other symmetry groups?

The point group 432 is a subgroup of the larger symmetry group O(3), which includes all possible symmetries in three dimensions. It is also related to other point groups, such as 432's subgroups 4, 3, and 2, which have lower degrees of symmetry.

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