l //8Bcap m %5`z 8L@7l4RHhCH_A=<d l4Hh l4<C l%Different generators for the group D8HH l4motif x@ %%@@5%A?8h 8L@7IX}T%HH!$Hd l  mG_.This exercise is to be done after the exercise on gereration of C8. On the left is the C8 pattern generated earlier by a 45 degree rotation, and L1 is a line through O, the center of rotation. On the right is a single motif with L1 and O in the same position as on the left, and a second line L2 through O. On the left, the select L1 and mark as mirror. Select the whole C8 design and reflect it in L1. Now open the D8 script, and place it at the upper right of the window so it doesn't obscure the sketch window. Select, in order (hold down the shift key) in the sketch on the right, the shaded interior (only) of the motif, L2, and L1. Play the script. It will reflect the motif first in one of the lines L1, L2, then the other, then repeat this to reflect the images, and so on, until the design is complete. Compare the design generated on right with that on the left. Although they were created with different sets of generators, they are the same (check this!). Measure the angle between L1 and L2 on the right. How is this related to the rotation that generates C8? In the completed designs, describe the orbits of each of the points X, Y, O. When completed with the investigation, close the sketch. Choose "Don't save" to restore it to its original state.e.e.When completed with the investigation, close the sketch. Choose "Don't save" to restore it to i&!8L@7Y2ˤ|ҀGenerators for D8=)P8 =TXlHH)49) 8L@7Y2ˤ|ҀCBXdUiZ) 8L@7B2ˤ|ҀBBrw 8L@7X2ˤ|ҀBCZr_w 8L@7D2ˤ|ҀBBv{ 8L@7O2ˤ|ҀBC"16q 8L@7A2ˤ|ҀCŀBLaZf_ 8L@7B2ˤ|ҀCBv{< 8L@7X2ˤ|ҀCC Yv^{ 8L@7D2ˤ|ҀCBzP8 8L@7O2ˤ|ҀCC!~ 8L@7C2ˤ|ҀCC53\m  8L@722ˤ|Ҁ?@CBCC CBCŀBL<! 8L@7i2ˤ|Ҁ6]O is the center of rotation; L1 and L2 are mirrors; L2 is the perpendicular bisector of XX''r of XX'h ghP Xh>T@$%9%83Ti  8L@7j2ˤ|ҀCBXBB?cTwW  8L@7k2ˤ|ҀBBBC?Yqw  8L@7m2ˤ|ҀBCBB?3q_  8L@7n2ˤ|ҀBBCBX?J4O9?I 8L@7A2ˤ|ҀBV BwH49?I 8L@7B2ˤ|ҀBXCzej?I 8L@7C2ˤ|ҀBCqBvG?I 8L@7D2ˤ|ҀBY#Bs0Yf  8L@7j12ˤ|ҀCŀBLCB? `Y{W  8L@7k12ˤ|ҀCBCC ? Xu{  8L@7m12ˤ|ҀCC CB? 0u^  8L@7n12ˤ|ҀCBCŀBL? u  8L@7s12ˤ|ҀCC CC5? ' / 8L@7L12ˤ|ҀCC!CC @ffffff '+) 8L@7L12ˤ|ҀBC"BC@3\  8L@772ˤ|Ҁ?CBCC CBCŀBL .3䝐 8L@7 BDUGHH@CIC= 16 8L@7 BBWl$WlU$K4CC ^c@'e 8L@7 AZW`UWC݊A; [`@ 8L@7 AYXWTt8ƀUUUU0HHBA I39?I  8L@7j2ˤ|ҀBV BwHBXCz?3j?I  8L@7k2ˤ|ҀBXCzBC?pAj?I  8L@7m2ˤ|ҀBCBY#Bs?I3vG?I  8L@7n2ˤ|ҀBY#BsBV BwH? ?I 8L@7A2ˤ|ҀA?C:??I 8L@7B2ˤ|ҀBoCCbg?I 8L@7C2ˤ|ҀBC&05?I 8L@7D2ˤ|ҀBHC&L6h!  8L@7222ˤ|Ҁ? BY#BsBCBXCzBV BwHPjUo[ 8L@7B22ˤ|ҀC#GBADW  8L@7 22ˤ|Ҁ?CBCC C؞BOCOBv']3H  8L@7L1idg"@ (0@ @@g lgdC݊A;CIC=?oOR!#Z6<  8L@7L1idg"@ (0@ @@g lgdCCBA?ɲl&$" ??I  8L@7j2ˤ|ҀA?CBoCC?%9g?I  8L@7k2ˤ|ҀBoCCBC&?&/g?I  8L@7m2ˤ|ҀBC&BHC&?' 5?I  8L@7n2ˤ|ҀBHC&A?C?( %?I 8L@7A2ˤ|ҀBCdw)ch?I 8L@7B2ˤ|ҀBCc*kp?I 8L@7C2ˤ|ҀB_bC2w+GL?I 8L@7D2ˤ|ҀBsCVSn, e?I  8L@722ˤ|Ҁ?BBHC&BC&BoCCA?C-h?I  8L@7j2ˤ|ҀBCdwBCc?2bp?I  8L@7k2ˤ|ҀBCcB_bC2w?3Fp?I  8L@7m2ˤ|ҀB_bC2wBsCVSn?4L?I  8L@7n2ˤ|ҀBsCVSnBCdw?5 hm?I 8L@7A2ˤ|ҀBC6?I 8L@7B2ˤ|ҀCC^7z?I 8L@7C2ˤ|ҀBC68z?I 8L@7D2ˤ|ҀBCh9"n?I  8L@722ˤ|Ҁ?lBBsCVSnB_bC2wBCcBCdw:g?I  8L@7j2ˤ|ҀBCCC^?;y?I  8L@7k2ˤ|ҀCC^BC6?<y?I  8L@7m2ˤ|ҀBC6BCh?=g?I  8L@7n2ˤ|ҀBChBC?>?I 8L@7A2ˤ|ҀC:wCxD\??I 8L@7B2ˤ|ҀC9C5@?I 8L@7C2ˤ|ҀCwC-POA?I 8L@7D2ˤ|ҀC,SnCPGBq  8L@7s12ˤ|ҀBCBC6?Aj?I  8L@722ˤ|Ҁ?HBChBC6CC^BCC?I  8L@7j2ˤ|ҀC:wCxD\C9C5?D?I  8L@7k2ˤ|ҀC9C5CwC-PO?E?I  8L@7m2ˤ|ҀCwC-POC,SnCPG?F?I  8L@7n2ˤ|ҀC,SnCPGC:wCxD\?G?I 8L@7A2ˤ|ҀCdC0H?I 8L@7B2ˤ|ҀC4CI?I 8L@7C2ˤ|ҀC CJ?I 8L@7D2ˤ|ҀC>CK?I  8L@722ˤ|Ҁ?,BC,SnCPGCwC-POC9C5C:wCxD\M~?I  8L@7j2ˤ|ҀCdC0C4C?N~?I  8L@7k2ˤ|ҀC4CC C?O?I  8L@7m2ˤ|ҀC CC>C?P?I  8L@7n2ˤ|ҀC>CCdC0?Q^c?I 8L@7A2ˤ|ҀCND\B]R^c?I 8L@7B2ˤ|ҀC BzfS?I 8L@7X'2ˤ|ҀCPOC Tlq?I 8L@7D2ˤ|ҀC&GBY#U?I  8L@722ˤ|Ҁ?POC,C>CC CC4CCdC0V]c?I  8L@7j2ˤ|ҀCND\B]C Bzf?W]?I  8L@7k2ˤ|ҀC BzfCPOC?Xk?I  8L@7m2ˤ|ҀCPOCC&GBY#?Y]q?I  8L@7n2ˤ|ҀC&GBY#CND\B]?Z`?I  8L@722ˤ|Ҁ?C&GBY#CPOCC BzfCND\B]_ 8L@7X'2ˤ|ҀCè'C ]6W?I  8L@722ˤ|Ҁ?ƜBBBCBBCBWdu!  8L@7k12ˤ|ҀCè'CCC ? e~ 8L@7A22ˤ|ҀCCg' Y 8L@7L22ˤ|ҀCC!CC@UUUUUUh $`)e"z 8L@7 BCUJHH@CٸCm i@ 8L@7 BAUW`HHCAm i_)fW  8L@7L2idg"@ (0@ @@g lgdCٸCmCAm?4R8 kj