Orthorhombic system
Axes length : a ≠ b ≠ c
Axial angles: α = β = δ= 90o
Elements of symmetry:
Axes of symmetry: 3 (a,b,c) axes
Planes of symmetry : 3m (1 Horizontal + 2 Vertical)
Center of symmetry: +ve
Crystal forms
1. Basal pinacoid (001) 2 faces
2. Front pinacoid (100) 2 faces
3. Side pinacoid (010) 2 faces
4. Orthorhombic prism (hk0) 4 faces
5. a-dome (0kL) 4 faces
6. b-dome (h0L) 4 faces
7. Orthorhombic bi-pyramid (hkL) 8 faces
Tetragonal system
Axes length : a = b ≠ c
Axial angles: α = β = δ= 90o
Elements of symmetry:
Axes of symmetry:
1 c,4 (2 (a,b) axes + 2 from Equitable)
Planes of symmetry :
5m (1 Horizontal + 4 Vertical)
Center of symmetry: +ve
Crystal forms
1. Basal pinacoid (001) 2 faces
2. Tetragonal prism 1st order (hh0) 4 faces
3. Tetragonal prism 2nd order (100) 4 faces
4. Di-tetragonal prism (hk0) 8 faces
5. Tetragonal bipyramid 1st order (hhL) 8 faces
6. Tetragonal bipyramid 2nd order (h0L) 8 faces
7. Di-tetragonal bipyramid (hkL) 16 faces
Cubic system
Axes length: a = b = C
Axial angles: α = β = δ= 90o
Elements of symmetry:
Axes of symmetry:
3 (a,b,c) axes, 4 from corners or solid angles,
6 from Equitable
Planes of symmetry :
9m (1 Horizontal + 4 Vertical + 4 Inclined)
Center of symmetry: +ve
Crystal forms
1. Cube (100) 6 faces
2. Octahedron (111) 8 faces
3. Rhombic Dodecahedron (110) 12 faces
4. Tetra-Hexahedron (hk0) 24 faces
5. Tris-octahedron (hhL) 24 faces
6. Icosi-tetrahedron (hLL) 24 faces
7. Hex-octahedron (hkL) 48 faces
Orthorhombic system Cubic system
1. Basal pinacoid (001) 2 faces 1. Cube (100) 6 faces
2. Front pinacoid (100) 2 faces 2. Octahedron (111) 8 faces
3. Side pinacoid (010) 2 faces 3. Rhombic Dodecahedron (110) 12 faces
4. Orthorhombic prism (hk0) 4 faces 4. Tetra-Hexahedron (hk0) 24 faces
5. a-dome (0kL) 4 faces 5. Tris-octahedron (hhL) 24 faces
6. b-dome (h0L) 4 faces 6. Icosi-tetrahedron (hLL) 24 faces
7. Orthorhombic bi-pyramid (hkL) 8 faces 7. Hex-octahedron (hkL) 48 faces
Tetragonal system
1. Basal pinacoid (001) 2 faces
2. Tetragonal prism 1st order (hh0) 4 faces
3. Tetragonal prism 2nd order (100) 4 faces
4. Di-tetragonal prism (hk0) 8 faces
5. Tetragonal bipyramid 1st order (hhL) 8 faces
6. Tetragonal bipyramid 2nd order (h0L) 8 faces
7. Di-tetragonal bipyramid (hkL) 16 faces
Hexagonal System
Axes length : a1= a2= a3 c
Axial angles: = = 90°, δ = 120°
Elements of symmetry:
Axes of symmetry:
1 c,6 (3 (a1, a2, a3 ) axes + 3 from Equitable)
Planes of symmetry :
7m (1 Horizontal + 6 Vertical)
Center of symmetry: +ve
Crystal forms
1. Basal Pinacoid (0001) 2 Faces
2. Hexagonal Prism first order (h0hˉ0) 6 faces
3. Hexagonal Prism second order (hh2hˉ0) 6 faces
4. Di-hexagonal Prism (hkiˉ0) (12) faces
5. Hexagonal Bi-Pyramid first order (h0hˉL) 12 faces
6. Hexagonal Bi-Pyramid second order (hh2hˉL) 12 faces
7. Di-hexagonal Bi-Pyramid (h k iˉL) 24 faces
Trigonal System
Axes length : a1= a2= a3 c
Axial angles: = = 90°, δ = 120°
Elements of symmetry:
Axes of symmetry:
1 c ,3 (a1, a2, a3 ) axes
Planes of symmetry :
3m = 3 Vertical Planes coincide on Equitable
Center of symmetry: +ve
Crystal forms
1. Basal Pinacoid (0001) 2 Faces
2. Hexagonal Prism first order (h0hˉ0) 6 faces
3. Hexagonal Prism second order (hh2hˉ0) 6 faces
4. Rhombohedron (h0hˉL) 6 Faces
5. Rhombohedron (0hhˉL) 6 Faces
6. Di-Trigonal Scalenohedron (h k iˉL) 12 faces
Crystal Systems
System No. of Axes Angles Unique Symmetry
axes lengths
Cubic a=b=c = = δ = 90° Three 4-fold axes
Tetragonal a=bc = = δ = 90° 4-fold axis with c
Three a, b (2-fold) axes
Orthorhombic axes a≠bc = = δ = 90° Three 2-fold axes
Monoclinic abc = δ= 90°, 90° 2-fold axis with b
Triclinic abc δ 90° None
Hexagonal a1= a2= a3 = = 90°, δ = 120° 6-fold axis with c
Four axes c a1= a2= a3 (2-fold) axes
Trigonal a1= a2= a3 = = 90°, δ = 120° 3ˉ-fold axis with c
c a1= a2= a3 (2-fold) axes
