<s>
In	O
2-dimensional	O
geometry	O
,	O
a	O
glide	B-Algorithm
reflection	I-Algorithm
(	O
or	O
transflection	B-Algorithm
)	O
is	O
a	O
symmetry	O
operation	O
that	O
consists	O
of	O
a	O
reflection	B-Algorithm
over	O
a	O
line	O
and	O
then	O
translation	B-Algorithm
along	O
that	O
line	O
,	O
combined	O
into	O
a	O
single	O
operation	O
.	O
</s>
<s>
The	O
intermediate	O
step	O
between	O
reflection	B-Algorithm
and	O
translation	B-Algorithm
can	O
look	O
different	O
from	O
the	O
starting	O
configuration	O
,	O
so	O
objects	O
with	O
glide	B-Algorithm
symmetry	I-Algorithm
are	O
in	O
general	O
,	O
not	O
symmetrical	O
under	O
reflection	B-Algorithm
alone	O
.	O
</s>
<s>
A	O
single	O
glide	O
is	O
represented	O
as	O
frieze	B-Algorithm
group	I-Algorithm
p11g	O
.	O
</s>
<s>
A	O
glide	B-Algorithm
reflection	I-Algorithm
can	O
be	O
seen	O
as	O
a	O
limiting	O
rotoreflection	B-Algorithm
,	O
where	O
the	O
rotation	O
becomes	O
a	O
translation	B-Algorithm
.	O
</s>
<s>
The	O
combination	O
of	O
a	O
reflection	B-Algorithm
in	O
a	O
line	O
and	O
a	O
translation	B-Algorithm
in	O
a	O
perpendicular	O
direction	O
is	O
a	O
reflection	B-Algorithm
in	O
a	O
parallel	O
line	O
.	O
</s>
<s>
However	O
,	O
a	O
glide	B-Algorithm
reflection	I-Algorithm
cannot	O
be	O
reduced	O
like	O
that	O
.	O
</s>
<s>
Thus	O
the	O
effect	O
of	O
a	O
reflection	B-Algorithm
combined	O
with	O
any	O
translation	B-Algorithm
is	O
a	O
glide	B-Algorithm
reflection	I-Algorithm
,	O
with	O
as	O
special	O
case	O
just	O
a	O
reflection	B-Algorithm
.	O
</s>
<s>
For	O
example	O
,	O
there	O
is	O
an	O
isometry	O
consisting	O
of	O
the	O
reflection	B-Algorithm
on	O
the	O
x-axis	O
,	O
followed	O
by	O
translation	B-Algorithm
of	O
one	O
unit	O
parallel	O
to	O
it	O
.	O
</s>
<s>
The	O
isometry	O
group	O
generated	O
by	O
just	O
a	O
glide	B-Algorithm
reflection	I-Algorithm
is	O
an	O
infinite	O
cyclic	O
group	O
.	O
</s>
<s>
Combining	O
two	O
equal	O
glide	B-Algorithm
reflections	I-Algorithm
gives	O
a	O
pure	O
translation	B-Algorithm
with	O
a	O
translation	B-Algorithm
vector	O
that	O
is	O
twice	O
that	O
of	O
the	O
glide	B-Algorithm
reflection	I-Algorithm
,	O
so	O
the	O
even	O
powers	O
of	O
the	O
glide	B-Algorithm
reflection	I-Algorithm
form	O
a	O
translation	B-Algorithm
group	I-Algorithm
.	O
</s>
<s>
In	O
the	O
case	O
of	O
glide	B-Algorithm
reflection	I-Algorithm
symmetry	I-Algorithm
,	O
the	O
symmetry	O
group	O
of	O
an	O
object	O
contains	O
a	O
glide	B-Algorithm
reflection	I-Algorithm
,	O
and	O
hence	O
the	O
group	O
generated	O
by	O
it	O
.	O
</s>
<s>
If	O
that	O
is	O
all	O
it	O
contains	O
,	O
this	O
type	O
is	O
frieze	B-Algorithm
group	I-Algorithm
p11g	O
.	O
</s>
<s>
Frieze	B-Algorithm
group	I-Algorithm
nr	O
.	O
</s>
<s>
6	O
(	O
glide-reflections	O
,	O
translations	O
and	O
rotations	O
)	O
is	O
generated	O
by	O
a	O
glide	B-Algorithm
reflection	I-Algorithm
and	O
a	O
rotation	O
about	O
a	O
point	O
on	O
the	O
line	O
of	O
reflection	B-Algorithm
.	O
</s>
<s>
A	O
typical	O
example	O
of	O
glide	B-Algorithm
reflection	I-Algorithm
in	O
everyday	O
life	O
would	O
be	O
the	O
track	O
of	O
footprints	O
left	O
in	O
the	O
sand	O
by	O
a	O
person	O
walking	O
on	O
a	O
beach	O
.	O
</s>
<s>
For	O
any	O
symmetry	O
group	O
containing	O
some	O
glide	B-Algorithm
reflection	I-Algorithm
symmetry	I-Algorithm
,	O
the	O
translation	B-Algorithm
vector	O
of	O
any	O
glide	B-Algorithm
reflection	I-Algorithm
is	O
one	O
half	O
of	O
an	O
element	O
of	O
the	O
translation	B-Algorithm
group	I-Algorithm
.	O
</s>
<s>
If	O
the	O
translation	B-Algorithm
vector	O
of	O
a	O
glide	B-Algorithm
reflection	I-Algorithm
is	O
itself	O
an	O
element	O
of	O
the	O
translation	B-Algorithm
group	I-Algorithm
,	O
then	O
the	O
corresponding	O
glide	B-Algorithm
reflection	I-Algorithm
symmetry	I-Algorithm
reduces	O
to	O
a	O
combination	O
of	O
reflection	B-Algorithm
symmetry	I-Algorithm
and	O
translational	O
symmetry	O
.	O
</s>
<s>
Glide	B-Algorithm
reflection	I-Algorithm
symmetry	I-Algorithm
with	O
respect	O
to	O
two	O
parallel	O
lines	O
with	O
the	O
same	O
translation	B-Algorithm
implies	O
that	O
there	O
is	O
also	O
translational	O
symmetry	O
in	O
the	O
direction	O
perpendicular	O
to	O
these	O
lines	O
,	O
with	O
a	O
translation	B-Algorithm
distance	O
which	O
is	O
twice	O
the	O
distance	O
between	O
glide	B-Algorithm
reflection	I-Algorithm
lines	O
.	O
</s>
<s>
If	O
there	O
are	O
also	O
true	O
reflection	B-Algorithm
lines	O
in	O
the	O
same	O
direction	O
then	O
they	O
are	O
evenly	O
spaced	O
between	O
the	O
glide	B-Algorithm
reflection	I-Algorithm
lines	O
.	O
</s>
<s>
A	O
glide	B-Algorithm
reflection	I-Algorithm
line	O
parallel	O
to	O
a	O
true	O
reflection	B-Algorithm
line	O
already	O
implies	O
this	O
situation	O
.	O
</s>
<s>
The	O
translational	O
symmetry	O
is	O
given	O
by	O
oblique	O
translation	B-Algorithm
vectors	O
from	O
one	O
point	O
on	O
a	O
true	O
reflection	B-Algorithm
line	O
to	O
two	O
points	O
on	O
the	O
next	O
,	O
supporting	O
a	O
rhombus	O
with	O
the	O
true	O
reflection	B-Algorithm
line	O
as	O
one	O
of	O
the	O
diagonals	O
.	O
</s>
<s>
In	O
3D	O
the	O
glide	B-Algorithm
reflection	I-Algorithm
is	O
called	O
a	O
glide	O
plane	O
.	O
</s>
<s>
It	O
is	O
a	O
reflection	B-Algorithm
in	O
a	O
plane	O
combined	O
with	O
a	O
translation	B-Algorithm
parallel	O
to	O
the	O
plane	O
.	O
</s>
<s>
In	O
the	O
Euclidean	O
plane	O
3	O
of	O
17	O
wallpaper	O
groups	O
require	O
glide	B-Algorithm
reflection	I-Algorithm
generators	O
.	O
</s>
<s>
p2gg	O
has	O
orthogonal	O
glide	B-Algorithm
reflections	I-Algorithm
and	O
2-fold	O
rotations	O
.	O
</s>
<s>
Glide	B-Algorithm
symmetry	I-Algorithm
can	O
be	O
observed	O
in	O
nature	O
among	O
certain	O
fossils	O
of	O
the	O
Ediacara	O
biota	O
;	O
the	O
machaeridians	O
;	O
and	O
certain	O
palaeoscolecid	O
worms	O
.	O
</s>
<s>
In	O
Conway	O
's	O
Game	O
of	O
Life	O
,	O
a	O
commonly	O
occurring	O
pattern	O
called	O
the	O
glider	O
is	O
so	O
named	O
because	O
it	O
repeats	O
its	O
configuration	O
of	O
cells	O
,	O
shifted	O
by	O
a	O
glide	B-Algorithm
reflection	I-Algorithm
,	O
after	O
two	O
steps	O
of	O
the	O
automaton	O
.	O
</s>
<s>
After	O
four	O
steps	O
and	O
two	O
glide	B-Algorithm
reflections	I-Algorithm
,	O
the	O
pattern	O
returns	O
to	O
its	O
original	O
orientation	O
,	O
shifted	O
diagonally	O
by	O
one	O
unit	O
.	O
</s>
