Question

Problem 3-4. 3-56 Determine the indices for the directions in the hexagonal lattice shown in Figure 3-43, using both the three-digit and four-digit systems. Figure 3-43 Directions in a hexagonal lattice for Problem 3.45

Answer 1

Answer

Solulien Direclion-A TLvee- dinit System .Tiooyoin , -1,6 and o, 0,0 a1e 2. o, -1,0-o,0 0-1,-1,0 3. No fralions to cle«r ch integers ta veduece Four- digit syadlem Convent t tree - oxis t e ere, tcieales indices in the tee -ani indices four digit syatem (hkilare : There fore, Ka-) 3

Hence, ncdices are Dise lion Three -clivit system ein are 1,1,0 and 0, o, . 3. No factios to cleak integers t veduce 4. Fo digt system Convert th 1tree -axis are h'1,k , L- Here, the indices in the theo - aris Terefore ndices in te fous - digit Satem (h k i 1) are

I elea faction hz1,kz1, iz-2, L--3 Hence, te ndices are Foun Now, we wi convet e Uree -axis o,, ' Hete, the iadices or te tLece -aniu ere fere, indices in e four -digit sqslem (a k i l)are Kk') 7h clear fraclsn hz-1, ko2,i--1, l - 2 e indices i 2ī3 Hence