problem in defining in k points and basis of traingular lattice

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Hi,
I have some doubt in the MPB  file tri-rod.ctl (reproduced here) ,a program
for triangular lattice.

(set! num-bands 8)

(set! geometry-lattice (make lattice (size 1 1 no-size)
                         (basis1 (/ (sqrt 3) 2) 0.5)
                         (basis2 (/ (sqrt 3) 2) -0.5)))
(set! geometry (list (make cylinder
                       (center 0 0 0) (radius 0.2) (height infinity)
                       (material (make dielectric (epsilon 12))))))

(set! k-points (list (vector3 0 0 0)          ; Gamma
                     (vector3 0 0.5 0)        ; M
                     (vector3 (/ -3) (/ 3) 0) ; K
                     (vector3 0 0 0)))        ; Gamma




*Why basis1 is not defined as basis1 ( 0.5 (/ (sqrt 3) 2)) and basis2
as basis2 ( 0.5 (/ (sqrt 3) -2)) if we refer the fig(enclosed here)
from the books" Photonic Crystal--Modelling the flow of light"?? *


*and while defining the k points also with the reciprocal lattice
vector, why it is not *

*                                                             vector3
0 0 0)          ; Gamma*

*                     (vector3 0 0.5 0)        ; M
                     (vector3 0.5 0.5 0)      ; K
                     (vector3 0 0 0)))        ; Gamma*

*since M point is half of b1, K point is half of b1 plus half of b2.*

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<div dir=3D"ltr"><div style=3D"color:rgb(34,34,34);font-family:arial,sans-s=
erif;font-size:13px;font-style:normal;font-variant:normal;font-weight:norma=
l;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px=
;text-transform:none;white-space:normal;word-spacing:0px;background-color:r=
gb(255,255,255)"><span class=3D"">Hi,<br>I </span>have some doubt in the MP=
B =C2=A0file tri-rod.ctl (reproduced here) ,a program for triangular lattic=
e.</div><div style=3D"color:rgb(34,34,34);font-family:arial,sans-serif;font=
-size:13px;font-style:normal;font-variant:normal;font-weight:normal;letter-=
spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-tra=
nsform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,25=
5,255)"><br></div><div style=3D"color:rgb(34,34,34);font-family:arial,sans-=
serif;font-size:13px;font-style:normal;font-variant:normal;font-weight:norm=
al;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0p=
x;text-transform:none;white-space:normal;word-spacing:0px;background-color:=
rgb(255,255,255)"><pre style=3D"white-space:pre-wrap">(set! num-bands 8)

(set! geometry-lattice (make lattice (size 1 1 no-size)
                         (basis1 (/ (sqrt 3) 2) 0.5)
                         (basis2 (/ (sqrt 3) 2) -0.5)))
(set! geometry (list (make cylinder
                       (center 0 0 0) (radius 0.2) (height infinity)
                       (material (make dielectric (epsilon 12))))))

(set! k-points (list (vector3 0 0 0)         =C2=A0; Gamma
                     (vector3 0 0.5 0)       =C2=A0; M
                     (vector3 (/ -3) (/ 3) 0)=C2=A0; K
                     (vector3 0 0 0)))       =C2=A0; Gamma</pre><pre style=
=3D"white-space:pre-wrap"><br></pre><pre style=3D"white-space:pre-wrap"><br=
></pre><pre style=3D"white-space:pre-wrap"><br></pre><pre style=3D"white-sp=
ace:pre-wrap"><b>Why basis1 is not defined as basis1 ( 0.5 <span style=3D"f=
ont-family:arial,sans-serif">(/ (sqrt 3) 2)) and=C2=A0</span><span style=3D=
"font-family:arial,sans-serif">basis2 as </span><span style=3D"font-family:=
arial,sans-serif">basis2 ( 0.5 </span><span style=3D"font-family:arial,sans=
-serif">(/ (sqrt 3) -2))=C2=A0</span><span style=3D"font-family:arial,sans-=
serif">if we refer the fig(enclosed here) from the books&quot; Photonic Cry=
stal--Modelling the flow of light&quot;</span><span style=3D"font-family:ar=
ial,sans-serif">?? </span></b></pre><pre style=3D"white-space:pre-wrap"><sp=
an style=3D"font-family:arial,sans-serif"><b><br></b></span></pre><pre styl=
e=3D"white-space:pre-wrap"><span style=3D"font-family:arial,sans-serif"><b>=
and while defining the k points also with the reciprocal lattice vector,=C2=
=A0why it is not </b></span></pre><pre style=3D"white-space:pre-wrap"><span=
 style=3D"font-family:arial,sans-serif"><b>                                =
                             vector3 0 0 0)         =C2=A0; Gamma</b></span=
></pre><pre style=3D"white-space:pre-wrap"><b>                     (vector3=
 0 0.5 0)       =C2=A0; M
                     (vector3 0.5 0.5 0)=C2=A0     ; K
                     (vector3 0 0 0)))       =C2=A0; Gamma</b></pre><pre st=
yle=3D"white-space:pre-wrap"><b>since M point is half of b1, K point is hal=
f of b1 plus half of b2.</b></pre><div><div><img src=3D"https://ssl.gstatic=
.com/ui/v1/icons/mail/images/cleardot.gif" class=3D""></div></div></div></d=
iv>

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