Hexagonal

The hexagonal lattice or triangular lattice is one of the five 2D lattice types. Three nearby points form an equilateral triangle. In images, four orientations of such a triangle are by far the most common.

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en.wikipedia.org

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glossary.periodni.com

Monoclinic

In the monoclinic system, the crystal is described by vectors of unequal lengths, as in the orthorhombic system. They form a rectangular prism with a parallelogram as its base. Hence two vectors are perpendicular (meet at right angles), while the third vector meets the other two at an angle other than 90°.

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en.wikipedia.org

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glossary.periodni.com

Orthorhombic

In crystallography, the orthorhombic crystal system is one of the 7 crystal systems. Orthorhombic lattices result from stretching a cubic lattice along two of its orthogonal pairs by two different factors, resulting in a rectangular prism with a rectangular base (a by b) and height (c), such that a, b, and c are distinct.

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en.wikipedia.org

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glossary.periodni.com

Tetragonal

In crystallography, the tetragonal crystal system is one of the 7 crystal systems. Tetragonal crystal lattices result from stretching a cubic lattice along one of its lattice vectors, so that the cube becomes a rectangular prism with a square base and height.

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en.wikipedia.org

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glossary.periodni.com

Trigonal and Triclinic

The triclinic lattice is the least symmetric of the 14 three-dimensional Bravais lattices. It has (itself) the minimum symmetry all lattices have: points of inversion at each lattice point and at 7 more points for each lattice point: at the midpoints of the edges and the faces, and at the center points.

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en.wikipedia.org

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gemsociety.org