Unit Cell: The smallest unit of a crystal that still retains all the physical, chemical and crystallographic properties of the mineral.

Symmetry operations: Movements performed on an object such that when completed, the object looks the same as when you started.

The 4 pure symmetry operations (which leave one point in the crystal unmoved) include:

1. Rotation Axis - An axis through the object, around which the object is rotated such that the original "motif" (or appearance) is repeated a specific number of times during 360 degrees

   Fold of Rotation	1	2	3	4	6
   Shorthand Notation		1A2	1A3	1A4	1A6
   Stereonet Symbol
   Degrees to Repeat Image	360	180	120	90	60

2. Mirror plane: plane passed through object such that the images on opposite sides of the plane
   are mirror images of one another

   Shorthand Notation	1m
   Stereonet Symbol	lines and primitive circle

3. Roto-inversion axis: first a rotation, then an inversion of 180 degrees

   Shorthand Notation
   Stereonet Symbol

4. Center of symmetry : if a line is extended from the center of an object a certain length in a certain direction, and another line of equal length but in the opposite direction, equivalent elements exist at both points.

   Shorthand Notation	i
   Stereonet Symbol	none

There are 32 possible combinations of the 4 pure symmetry elements that exist in nature. These make up the 32crystal classes. Crystal classes are grouped into 6 crystal systems based on shared symmetry.

Crystal systems:

System Name	Shared Symmetry	Axial Lengths	Angles
triclinic	i or none
monoclinic	1A2 and/or 1m
orthorhombic	3A2 and/or 1A22m
tetragonal	1A4
hexagonal	hex:1A6 rhomb:1A3	hex: rhomb:
isometric	4A3

*note: largest number of mineral species is concentrated in the crystal class with the highest symmetry of each system. These classes with the highest symmetry in each system are called "holohedral classes". They include:

the Pinacoidal Class for the Triclinic System
the Prismatic Class for the Monoclinic System
the Rhombic Dipyramidal Class for the Orthorhombic System
the Ditetragonal Dipyramidal Class for the Tetragonal System
the Hexagonal Scalenohedral Class for the Hex/Rhombohedral System
the Dihexagonal Dipyramidal Class for the Hex/Hexagonal System
and the Hexoctahedral Class for the Isometric System.

---

5 planar nets (2-dimensional atomic arrangements)

Oblique t1 < t2	Rectangular t1 < t2
Square t1 = t2	Rhombic t1 = t2

Centered rectangular is formed by

connecting the shared corners & centers of two adjacent rectangles. i.e.,

14 Bravais Lattices (3-dimensional atomic arrangements)

Formed by extending planar nets into 3rd dimension. Atom positions within Bravais Lattices can occur as follows:

• P - primitive: atoms only at corners
• F - face-centered: atoms at center of each face
• C - 2-face-centered: atoms at two opposite faces
• I(R) - body centered: atom at very center

---

Law of Constancy of Interfacial Angles: regardless of deformation during formation, all angles between faces will be perfect

Zone: if the faces of a crystal intercept to form edges and those edges are parallel - they form a zone

• most minerals are monoclinic or orthorhombic - 75%
• isometrics - 12.2%

---

http://classes.colgate.edu/rapril/geol201/ Questions to: rapril@mail.colgate.edu Copyright 1997 © Colgate University.

Mineralogy Home page