INDEX

*S*^{n}
*n*-dimensional absolute space

*E*^{n}, *L*^{n}
*n*-dimensional Euclidean and Lobachevsky's
space

*H*
subgroup

{*S*_{1},*S*_{2},¼,*S*_{n}}
set of generators

*G*×*G*_{1}
direct product of groups *G*, *G*_{1}

*C*_{n}, *D*_{n}
cyclic and dihedral group

*int*
interior

*Cl*
closure

{*p*,*q*}
regular tessellation

*X*, *Y*, *Z*
translation

*P*, *Q*, *O*
glide reflection

*G*_{nst¼}
Bohm symbols of symmetry group categories

*K* = *K*(*k*)
dilatation with coefficient *k*

*L* = *L*(*k*,q)
dilative rotation with coefficient *k* and
dilative rotation angle q

*M* = *M*(*k*,**m**)
dilative reflection with coefficient *k* and
reflection line **m**

*E*^{2}\{*O*}
*E*^{2} plane without point *O*

*R*_{I}
inversion

*Z*_{I}
inversional reflection

*S*_{I}
inversional rotation

*G*/*H*, *G*/*H*/*H*_{1}
group/subgroup symbols of antisymmetry
and colored symmetry groups

[*G*:*H*]=*N*
*H* is subgroup of index *N* of group *G*

(*k*,*m*) = 1
*k*, *m* are coprime numbers

**p _{0}**
continuous line group of translations

[*p*,*q*]
symmetry group of regular tessellation {*p*,q}

**p _{00}**
continuous plane group of translations

**m _{I}**
inversion circle