- (also
called rotation-reflection, rotoreflection,
rotary reflection, or
rotoinversion) is an
isometry in
Euclidean space that is a
combination of a rotation...
- Hermann–Mauguin
symbols show
rotoinversion axes,
unlike Schoenflies and
Shubnikov notations, that
shows rotation-reflection axes. The
rotoinversion axes are represented...
- may only
contain one-, two-, three-, four- and
sixfold rotations or
rotoinversions. This
reduces the
number of
crystallographic point groups to 32 (from...
-
system uses
rotoreflections (given the
symbol SR)
instead of
rotoinversions. For each
rotoinversion operation,
there is an
equivalent rotoreflection; examples...
- the
space group is Fd3m then δ=ε and ζ=0. In this case, a three-fold
rotoinversion with axis in the 111
direction is
centred on the
point (0, 0, 0) (where...
-
hence Sn = Cnh for odd n. Cni has only a
rotoinversion axis. This
notation is
rarely used
because any
rotoinversion axis can be
expressed instead as rotation-reflection...
-
operations of reflection,
rotation and
improper rotation (also
called rotoinversion), and the **** axis and
glide plane symmetry operations. The combination...
- {\displaystyle {\overline {3}}} is the Hermann–Mauguin
notation for a
threefold rotoinversion, used in crystallography. [ 1 ¯ 1 2 ¯ ] {\displaystyle [{\overline {1}}1{\overline...
-
represent an
inversion through the
origin and a
rotoinversion, respectively,
about the z-axis.
Rotations become more
complicated in...
-
point groups,
which include only rotations, reflections,
inversions and
rotoinversions – i.e., the
finite subgroups of O(n); (2)
infinite lattice groups, which...
