A092240 a(n) is the number of n-dimensional symmetry frieze designs (incorrect).

7, 17, 230, 4783

Offset: 1

Author

Nitsa Movshovitz-Hadar (nitsa(AT)tx.technion.ac.il), Oct 24 2004

Keywords

• dead

Comments

I suspect that some of the contributors to this entry have confused it with A004029. The term 4783 is probably wrong, since A004029(4) = 4783. - N. J. A. Sloane, Dec 27 2014

As far as I can tell, the values given in this sequence are not consistent with any possible interpretation of "Frieze". The standard Frieze groups are defined as the 2-D line groups (planar symmetry groups having a translation in one direction only). In one dimension, there are only 2 line groups (not 7), and 0 if we discount the groups having a translation in one direction (both of them). In three dimensions, there are the 219 or 230 crystallographic groups (depending on whether chiral copies are considered distinct), but these have translations in 3 directions. If we count groups having fewer than 3 translations, then there are just 80 layer groups (having translations in two directions), and 75 rod groups (having translations in one direction). - Brian Galebach, Oct 18 2016

Examples

			There are 7 strip patterns, i.e., 1-dimensional symmetry frieze designs; 17 wallpaper designs, i.e., 2-dimensional symmetry groups; 230 is the number of crystallographic groups, i.e., 3-dimensional symmetry designs; 4783 is the 4-dimensional extension of the above.
		

References

• Piergiorgio Odifreddi, The Mathematical Century: The 30 Greatest Problems of the Last 100 Years, Princeton University Press, 2004, see p. 102.

Links

• Yanxi Liu, Collins, R.T., Tsin, Y., A computational model for periodic pattern perception based on frieze and wallpaper groups, IEEE Trans. Pattern Analysis and Machine Intelligence, 26 (2004), 354-371.

Crossrefs

Cf. A004029, A006227.