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Number of "pieces" of the n-th Brillouin zone of a 2D square lattice.
2

%I #14 Jun 21 2022 10:28:03

%S 1,4,8,12,20,20,12,12,20,28,44,48,48

%N Number of "pieces" of the n-th Brillouin zone of a 2D square lattice.

%C Each Brillouin zone has the same area, and they are all equivalent mod the periodicity of the lattice, but the higher-order ones consist of a set of polygons. This is the number of polygons in that set.

%H Jaroslaw W. Klos, <a href="https://demonstrations.wolfram.com/2DBrillouinZones/">2D Brillouin Zones</a>, Wolfram Demonstrations Project, 2013.

%e The 2nd Brillouin zone consists of 4 right isosceles triangles, so a(2) = 4. The 4th Brillouin zone consists of 8 triangles and 4 kites, so a(4) = 12.

%Y Cf. A180604, A199765, A199766.

%K nonn,more

%O 1,2

%A _Keenan Pepper_, Sep 11 2010