Index

1 stand s 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 , 9 0

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 alway s 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. , 4 8

finite figure, 2 8

fixed point , 2 3

footprints, 4 2

fundamental domain , 11

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, 19

mirror line , 19

mod, 6 3

modular arithmetic , 9 1

addition, 6 3

multiplication, 6 5

101