Index 1 stands fo r do-nothing , 3 2 15-puzzle, 9 0 2-cycle, 7 1 addition mo d n , 6 3 alternating group , 9 0 AJV, alternatin g group , 90 associative operation , 5 3 basic unit , 8 , 4 9 bilateral symmetry , 3 8 Cayley diagram , 7 3 Cayley, Arthur , 6 7 closed path , 9 3 CN cyclic group, 6 1 symmetry type , 3 6 Conway, Joh n H , 4 2 crystallographic restriction , 5 2 cycle, 68 cyclic group, C/v , 6 1 dihedral group , DN, 6 1 DN dihedral group , 6 1 symmetry type , 3 7 do-nothing denoted b y 1 , 32 is a rotation an d a translation , is always a symmetry , 2 7 dual, 9 5 equivalent mirror lines , 4 7 rotocenter, 4 4 Escher, M.C. , 4 8 even permutation , 9 0 exponents rules of, 3 2 Fedorov, E.S. , 48 finite figure, 2 8 fixed point , 2 3 footprints, 4 2 fundamental domain , 1 1 generator, 73 , 92 glide line, 2 2 glide reflection , 2 2 phantom figure, 2 2 group, 51 , 53 AN, alternatin g group , 9 0 CN, cycli c group, 6 1 DN, dihedra l group , 6 1 generators, 7 3 presentation, 9 2 relation, 9 2 SN, symmetri e group , 68 identity matrix , 9 2 inverse, 35 , 38 isomorphism, 7 1 Kali, 53 , 98 Lloyd, Sam , 9 1 magie square , 9 6 matrix, 9 1 mirror, 1 9 mirror line , 1 9 mod, 6 3 modular arithmetic , 9 1 addition, 6 3 multiplication, 6 5 101

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