(Part Fifteen)

We continue our investigation concerning the generation of group elements of the Plane Groups.

In order to generate the group elements of the Plane Group P31m we will use an enlarged version of the last Figure (Figure 23) of the previous document.

Figure 1. *Magnification of Figure 23 of the previous document.
The *

The initial element

The generator

The generator

The generator

The next Figure shows the generation of the rest of the group elements at the lattice point

Figure 2. *Generation of the group elements ***p ^{2} , pm, **

Figure 3. *Completion of the second row of motifs s.l., i.e. all the group elements of this row are now generated.*

The next Figure indicates the rotations that can be performed on the newly generated elements, i.e. anticlockwise rotations of 120

Figure 4. *Indication of the rotations about the point ***R*** for generating new elements in the first and third row of motifs s.l.*

Figure 5. *The first and third row of motifs s.l. of our ***P31m*** pattern have been reached by rotations, and new group elements are generated.*

These first and third rows can now be filled in by means of translations

Figure 6. *Completion of the first and third rows of motifs s.l.*

The next Figure indicates how the fourth row of motifs s.l. can be reached by an anticlockwise rotation of 240

Figure 7. *Indication how the elements of the fourth row of motifs s.l. can be reached by a rotation.*

Figure 8. *The fourth row is reached by the rotation ***p ^{2}**

The fourth row can now be completed by means of translations

Figure 9. *Completion of the fourth row of motifs s.l. of the ***P31m*** pattern, by applying translations.*

We now have generated all group elements of the displayed part of the

In the

**e-mail :**

To continue click HERE

`back to the Ink-in-Glycerine Model`

`back to Part I of The Crystallization process and the Implicate Order`

`back to Part II of The Crystallization process and the Implicate Order`

`back to Part III of The Crystallization process and the Implicate Order`

`back to Part IV of The Crystallization process and the Implicate Order`

`back to Part V of The Crystallization process and the Implicate Order`

`back to Part VI of The Crystallization process and the Implicate Order`

`back to Part VII of The Crystallization process and the Implicate Order`

`back to Part VIII of The Crystallization process and the Implicate Order`

`back to Part IX of The Crystallization process and the Implicate Order`

`back to Part X of The Crystallization process and the Implicate Order`

`back to Part XI of The Crystallization process and the Implicate Order`

`back to Part XII of The Crystallization process and the Implicate Order`

`back to Part XIII of The Crystallization process and the Implicate Order`

`back to Part XIV of The Crystallization process and the Implicate Order`