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What kind of plane lattice is this?
Square

What kind of plane lattice is this?
Rectangle

What kind of plane lattice is this?
Diamond

Hexagonal

What kind of plane lattice is this?
Oblique

What kind of crystal system is this?
Cubic

What kind of crystal system is this?
Rhombohedral

What kind of crystal system is this?
Hexagonal

What kind of crystal system is this?
Tetragonal

What kind of crystal system is this?
Orthorhombic

What kind of crystal system is this?
Monoclinic

What kind of crystal system is this?
Triclinic
What are soft brackets () used for in notation?
Identifying planes/crystal faces
Whar are hard brackets [] used for in notation?
Identifying lattice direction.
What are fancy brackets {} used for in notation?
Identifying a family of lattice planes.
What are the common symmetry elements for a triclinic crystal?
One fold rotation with or without inversion.
What are the common symmetry elements for a monoclinic crystal?
Two fold rotation axis and/or a single mirror.
What are the common symmetry elements for a orthorhombic crystal?
Three 2 fold rotation axes, or two mirrors and a two fold axis.
What are the common symmetry elements for a tetragonal crystal?
Single 4 fold rotation or rotoinversion axis.
What are the common symmetry elements for a trigonal division-hexagonal crystal?
One 3 fold rotation axis.
What are the common symmetry elements for a hexagonal division-hexagonal crystal?
One 6 fold rotation axis.
What are the common symmetry elements for a isometric crystal?
Four 3-fold rotation axes oriented diagonally through the center of the unit cell from corner to corner.