netket.symmetry.group.axial

3D axial symmetry groups and transformations.

This module provides functions to construct point groups and symmetry operations for 3D systems with axial symmetry, including rotations, reflections, inversions, and their combinations. It includes common point groups like cyclic (C), dihedral (D), pyramidal (Cv), prismatic (Dh), and antiprismatic (Dd) groups.

Functions

C(n[, axis])	Returns the \(C_n\) PointGroup of rotations around a given axis.
Ch(n[, axis])	Returns the reflection group \(C_{nh}\) generated by an n-fold rotation axis and a reflection across the plane normal to the same axis.
Cv(n[, axis, axis2])	Returns the pyramidal group \(C_{nv}\) generated by an n-fold rotation axis and a reflection across a plane that contains the same axis.
D(n[, axis, axis2])	Returns the dihedral group \(D_n\) generated by an n-fold rotation axis and a twofold rotation axis perpendicular to the former.
Dd(n[, axis, axis2])	Returns the antiprismatic group \(D_{nd}\) generated by a 2*n*-fold roto- reflection axis and a reflection across a plane that contains the same axis.
Dh(n[, axis, axis2])	Returns the prismatic group \(D_{nh}\) generated by an n-fold rotation axis, a twofold rotation axis perpendicular to the former, and a mirror plane normal to the n-fold axis.
S(n[, axis])	Returns the \(S_n\) PointGroup of rotoreflections around a given axis.
antiprismatic(n[, axis, axis2])	Returns the antiprismatic group \(D_{nd}\) generated by a 2*n*-fold roto- reflection axis and a reflection across a plane that contains the same axis.
cuboid()	Symmetry group of a cuboid with edges aligned with the Cartesian axes.
cuboid_rotations()	Rotational symmetries of a cuboid with edges aligned with the Cartesian axes.
dihedral(n[, axis, axis2])	Returns the dihedral group \(D_n\) generated by an n-fold rotation axis and a twofold rotation axis perpendicular to the former.
glide(axis, trans[, origin])	Returns a glide composed of translation by trans and a reflection across a plane that passes through origin and is normal to axis.
glide_group(axis, trans[, origin])	Returns the Z_2 PointGroup containing the identity and a glide composed of translation by trans and a reflection across a plane that passes through origin and is normal to axis.
inversion()	Returns a 3D inversion as a PGSymmetry.
inversion_group()	\(\mathbb{Z}_2\) PointGroup containing the identity and inversion across the origin.
prismatic(n[, axis, axis2])	Returns the prismatic group \(D_{nh}\) generated by an n-fold rotation axis, a twofold rotation axis perpendicular to the former, and a mirror plane normal to the n-fold axis.
pyramidal(n[, axis, axis2])	Returns the pyramidal group \(C_{nv}\) generated by an n-fold rotation axis and a reflection across a plane that contains the same axis.
reflection(axis)	Returns a 3D reflection across a plane whose normal is axis.
reflection_group(axis)	Returns the \(\mathbb{Z}_2\) PointGroup containing the identity and a reflection across a plane with normal axis
rotation(angle, axis)	Returns a rotation by angle degrees around axis.
rotation_group(n[, axis])	Returns the \(C_n\) PointGroup of rotations around a given axis.
rotoreflection(angle, axis)	Returns a rotoreflection by angle degrees around axis.
screw(angle, trans[, origin])	Returns a screw composed of a translation by trans and a rotation by angle degrees around its direction.
screw_group(angle, trans[, origin])	Returns the PointGroup generated by a screw composed of a translation by trans and a rotation by angle degrees around its direction.