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
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