Notation

n

1

2

3

4

6

C_n

C₁

C₂

C₃

C₄

C₆

C_nv

C_1v=C_1h

C_2v

C_3v

C_4v

C_6v

C_nh

C_1h

C_2h

C_3h

C_4h

C_6h

D_n

D₁=C₂

D₂

D₃

D₄

D₆

D_nh

D_1h=C_2v

D_2h

D_3h

D_4h

D_6h

D_nd

D_1d=C_2h

D_2d

D_3d

D_4d

D_6d

S_2n

S₂

S₄

S₆

S₈

S₁₂

1

1

2

²⁄_m

222

m

mm2

mmm

3

3

32

3m

3m

4

4

⁴⁄_m

422

4mm

42m

⁴⁄_mmm

6

6

⁶⁄_m

622

6mm

62m

⁶⁄_mmm

23

m3

432

43m

m3m

Crystal family

Crystal system

Hermann-Mauguin (full symbol)

Hermann-Mauguin (short symbol)

Shubnikov^[1]

Schoenflies

Orbifold

Coxeter

Order

Triclinic

1

1

C₁

11

[ ]⁺

1

1

1

C_i = S₂

x

[2⁺,2⁺]

2

Monoclinic

2

2

C₂

22

[2]⁺

2

m

m

C_s = C_1h

*

[ ]

2

2/m

C_2h

2*

[2,2⁺]

4

Orthorhombic

222

222

D₂ = V

222

[2,2]⁺

4

mm2

mm2

C_2v

*22

[2]

4

mmm

D_2h

*222

[2,2]

8

Tetragonal

4

4

C₄

44

[4]⁺

4

4

4

S₄

2x

[2⁺,4⁺]

4

4/m

C_4h

4*

[2,4⁺]

8

422

422

D₄

422

[4,2]⁺

8

4mm

4mm

C_4v

*44

[4]

8

42m

42m

D_2d

2*2

[2⁺,4]

8

4/mmm

D_4h

*422

[4,2]

16

Hexagonal

Trigonal

3

3

C₃

33

[3]⁺

3

3

3

S₆ = C_3i

3x

[2⁺,6⁺]

6

32

32

D₃

322

[3,2]⁺

6

3m

3m

C_3v

*33

[3]

6

3

3m

D_3d

2*3

[2⁺,6]

12

Hexagonal

6

6

C₆

66

[6]⁺

6

6

6

C_3h

3*

[2,3⁺]

6

6/m

C_6h

6*

[2,6⁺]

12

622

622

D₆

622

[6,2]⁺

12

6mm

6mm

C_6v

*66

[6]

12

6m2

6m2

D_3h

*322

[3,2]

12

6/mmm

D_6h

*622

[6,2]

24

Cubic

23

23

T

332

[3,3]⁺

12

3

m3

T_h

3*2

[3⁺,4]

24

432

432

O

432

[4,3]⁺

24

43m

43m

T_d

*332

[3,3]

24

3

m3m

O_h

*432

[4,3]

48

Crystal System

Crystal Class

Symmetry

Name of Class

1

none

Pedial

i

Pinacoidal

Monoclinic

2

1A₂

Sphenoidal

m

1m

Domatic

2/m

i, 1A₂, 1m

Prismatic

Orthorhombic

222

3A₂

Rhombic-disphenoidal

mm2 (2mm)

1A₂, 2m

Rhombic-pyramidal

2/m2/m2/m

i, 3A₂, 3m

Rhombic-dipyramidal

4

1A₄

Tetragonal- Pyramidal

₄

Tetragonal-disphenoidal

4/m

i, 1A₄, 1m

Tetragonal-dipyramidal

422

1A₄, 4A₂

Tetragonal-trapezohedral

1A₄, 4m

Ditetragonal-pyramidal

2m

1₄, 2A₂, 2m

Tetragonal-scalenohedral

4/m2/m2/m

i, 1A₄, 4A₂, 5m

Ditetragonal-dipyramidal

1A₃

Trigonal-pyramidal

33

Rhombohedral

32

1A₃, 3A₂

Trigonal-trapezohedral

1A₃, 3m

Ditrigonal-pyramidal

2/m

1₃, 3A₂, 3m

Hexagonal-scalenohedral

6

1A₆

Hexagonal-pyramidal

66

Trigonal-dipyramidal

6/m

i, 1A₆, 1m

Hexagonal-dipyramidal

622

1A₆, 6A₂

Hexagonal-trapezohedral

1A₆, 6m

Dihexagonal-pyramidal

m2

1₆, 3A₂, 3m

Ditrigonal-dipyramidal

6/m2/m2/m

i, 1A₆, 6A₂, 7m

Dihexagonal-dipyramidal

3A₂, 4A₃ 

Tetaroidal

2/m

3A₂, 3m, 4₃ 

Diploidal

3A₄, 4A₃, 6A₂

Gyroidal

3m

3₄, 4A₃, 6m

Hextetrahedral

3A₄, 4₃, 6A₂, 9m

Hexoctahedral

http://www.tulane.edu/~sanelson/eens211/32crystalclass.htm

the 32 crystal classes are divided into 6 crystal systems.

1. The Triclinic System has only 1-fold or 1-fold rotoinversion axes.

2. The Monoclinic System has only mirror plane(s) or a single 2-fold axis.

3. The Orthorhombic System has only two fold axes or a 2-fold axis and

2 mirror planes.

4. The Tetragonal System has either a single 4-fold or 4-fold

rotoinversion axis.

5. The Hexagonal System has no 4-fold axes, but has at least 1 6-fold

or 3-fold axis.

6. The Isometric System has either 4 3-fold axes or 4 3-fold rotoinversion

axes.

The Wilson cycle begins in Stage A with a stable continental craton. A hot spot (not present in the drawings) rises up under the craton, heating it, causing it to swell upward, stretch and thin like taffy, crack, and finally split into two pieces. This process not only splits a continent in two it also creates a new divergent plate boundary.      Stage B - the one continent has been separated into two continents, east and west, and a new ocean basin (the Ophiolite Suite) is generated between them. The ocean basin in this stage is comparable to the Red Sea today. As the ocean basin widens the stretched and thinned edges where the two continents used to be joined cool, become denser, and sink below sea level. Wedges of divergent continental margins sediments accumulate on both new continental edges.      Stage C - the ocean basin widens, sometimes to thousands of miles; this is comparable to the Atlantic ocean today. As long as the ocean basin is opening we are still in the opening phase of the Wilson cycle.     Stage D - the closing phase of the Wilson Cycle begins when a subduction zone (new convergent plate boundary) forms. The subduction zone may form anywhere in the ocean basin, and may face in any direction. In this model we take the simplest situation; a subduction zone developing under the edge of one continent. Once the subduction zone is active the ocean basin is doomed; it will all eventually subduct and disappear. These are remnant ocean basins.      Stage E - most of the remnant ocean basin has subducted and the two continents are about to collide. Subduction under the edge of a continent has a lot of results. Deep in the subduction zone igneous magma is generated and rises to the surface to form volcanoes, that build into a cordilleran mountain range (e.g. the Cascade mountains of Washington, Oregon, and northern California.) Also, a lot of metamorphism occurs and folding and faulting.     Stage F - the two continents, separated in Stages A and B now collide. The remnant ocean basin is completely subducted. Technically the closing phase of the Wilson cycle is over. Because the subduction zone acts as a ramp the continent with the subduction zone (a hinterland) slides up over the edge of the continent without it (a foreland).     Stage G - once the collision has occurred the only thing left for the mountain to do is erode down to sea level - a peneplain. The stage G drawing is a distortion, however. With the collision the continental thickness doubles, and since continental rock is light weight, both will rise as the mountain erodes, much like a boat rises when cargo is taken off of it. Thus, in reality, most of the hinterland continent will be eroded away, and the foreland continent will eventually get back to the earth's surface again.