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Point groups in three dimensions
In
geometry
, a
point group
in three dimensions
is an
isometry group
in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a
sphere
. It is a
subgroup
of the
orthogonal group
O(3), the group of all
isometries
that leave the origin fixed, or correspondingly, the group of
orthogonal matrices
. O(3) itself is a subgroup of the
Euclidean group
E
(3) of all isometries.
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