Triclinic (aP) Monoclinic (mP) Monoclinic (mC) Orthorhombic (oP) Orthorhombic (oI) Orthorhombic (oF) Orthorhombic (oC) Tetragonal (tP) Tetragonal (tI) Hexagonal (hP) Rhombohedral (hR) [hP and hR] Cubic (cP) Cubic (cI) Cubic (cF) A crystal, which has a regularly repeating pattern of atoms, may be represented by a lattice - a set of points which have identical surroundings. Thus, for a crystal, each lattice point is surrounded by the same geometrical arrangement of atoms. Bravais lattices are named after Auguste Bravais who, in 1848, described fourteen distinct three-dimensional arrangements of lattice points. The Bravais lattices are classified by symmetry and centring, and all fourteen may be shown by clicking the buttons above. Six symmetries are defined: triclinic (a - for anorthic), monoclinic (m), orthorhombic (o), tetragonal (t), hexagonal or trigonal (h) and cubic (c). Primitive (P) and rhombohedral (R) have lattice points at corners only. Additional lattice points are required at centres of opposite unit cell faces for centred lattices (A, B, or C faces), at centres of all faces for face centred lattices (F), and at body centres for 'Innenzentrierte' lattices (I). Each Bravais lattice is defined by three unit cell coordinates (a,b and c) and by angles between these coordinates, a (between b and c), b (between a and c) and g (between a and b). The symmetries place restrictions on these coordinates and angles as follows: Triclinic no restrictions Monoclinic a=g=90o Orthorhomic a=b=g=90o Tetragonal a=b=g=90o a=b Hexagonal a=b=90o g=120o a=b Rhombohedral a=b=g<120o a=b=c Cubic a=b=g=90o a=b=c Click and hold the mouse over the CHIME image, then move the mouse to rotate the Bravais lattice displayed. The origin is highlighted by a red sphere.
Monoclinic (mP) Monoclinic (mC) Orthorhombic (oP) Orthorhombic (oI) Orthorhombic (oF) Orthorhombic (oC) Tetragonal (tP) Tetragonal (tI) Hexagonal (hP) Rhombohedral (hR) [hP and hR] Cubic (cP) Cubic (cI) Cubic (cF) A crystal, which has a regularly repeating pattern of atoms, may be represented by a lattice - a set of points which have identical surroundings. Thus, for a crystal, each lattice point is surrounded by the same geometrical arrangement of atoms. Bravais lattices are named after Auguste Bravais who, in 1848, described fourteen distinct three-dimensional arrangements of lattice points. The Bravais lattices are classified by symmetry and centring, and all fourteen may be shown by clicking the buttons above. Six symmetries are defined: triclinic (a - for anorthic), monoclinic (m), orthorhombic (o), tetragonal (t), hexagonal or trigonal (h) and cubic (c). Primitive (P) and rhombohedral (R) have lattice points at corners only. Additional lattice points are required at centres of opposite unit cell faces for centred lattices (A, B, or C faces), at centres of all faces for face centred lattices (F), and at body centres for 'Innenzentrierte' lattices (I). Each Bravais lattice is defined by three unit cell coordinates (a,b and c) and by angles between these coordinates, a (between b and c), b (between a and c) and g (between a and b). The symmetries place restrictions on these coordinates and angles as follows: Triclinic no restrictions Monoclinic a=g=90o Orthorhomic a=b=g=90o Tetragonal a=b=g=90o a=b Hexagonal a=b=90o g=120o a=b Rhombohedral a=b=g<120o a=b=c Cubic a=b=g=90o a=b=c Click and hold the mouse over the CHIME image, then move the mouse to rotate the Bravais lattice displayed. The origin is highlighted by a red sphere.
Orthorhombic (oP) Orthorhombic (oI) Orthorhombic (oF) Orthorhombic (oC) Tetragonal (tP) Tetragonal (tI) Hexagonal (hP) Rhombohedral (hR) [hP and hR] Cubic (cP) Cubic (cI) Cubic (cF) A crystal, which has a regularly repeating pattern of atoms, may be represented by a lattice - a set of points which have identical surroundings. Thus, for a crystal, each lattice point is surrounded by the same geometrical arrangement of atoms. Bravais lattices are named after Auguste Bravais who, in 1848, described fourteen distinct three-dimensional arrangements of lattice points. The Bravais lattices are classified by symmetry and centring, and all fourteen may be shown by clicking the buttons above. Six symmetries are defined: triclinic (a - for anorthic), monoclinic (m), orthorhombic (o), tetragonal (t), hexagonal or trigonal (h) and cubic (c). Primitive (P) and rhombohedral (R) have lattice points at corners only. Additional lattice points are required at centres of opposite unit cell faces for centred lattices (A, B, or C faces), at centres of all faces for face centred lattices (F), and at body centres for 'Innenzentrierte' lattices (I). Each Bravais lattice is defined by three unit cell coordinates (a,b and c) and by angles between these coordinates, a (between b and c), b (between a and c) and g (between a and b). The symmetries place restrictions on these coordinates and angles as follows: Triclinic no restrictions Monoclinic a=g=90o Orthorhomic a=b=g=90o Tetragonal a=b=g=90o a=b Hexagonal a=b=90o g=120o a=b Rhombohedral a=b=g<120o a=b=c Cubic a=b=g=90o a=b=c Click and hold the mouse over the CHIME image, then move the mouse to rotate the Bravais lattice displayed. The origin is highlighted by a red sphere.
Tetragonal (tP) Tetragonal (tI) Hexagonal (hP) Rhombohedral (hR) [hP and hR] Cubic (cP) Cubic (cI) Cubic (cF) A crystal, which has a regularly repeating pattern of atoms, may be represented by a lattice - a set of points which have identical surroundings. Thus, for a crystal, each lattice point is surrounded by the same geometrical arrangement of atoms. Bravais lattices are named after Auguste Bravais who, in 1848, described fourteen distinct three-dimensional arrangements of lattice points. The Bravais lattices are classified by symmetry and centring, and all fourteen may be shown by clicking the buttons above. Six symmetries are defined: triclinic (a - for anorthic), monoclinic (m), orthorhombic (o), tetragonal (t), hexagonal or trigonal (h) and cubic (c). Primitive (P) and rhombohedral (R) have lattice points at corners only. Additional lattice points are required at centres of opposite unit cell faces for centred lattices (A, B, or C faces), at centres of all faces for face centred lattices (F), and at body centres for 'Innenzentrierte' lattices (I). Each Bravais lattice is defined by three unit cell coordinates (a,b and c) and by angles between these coordinates, a (between b and c), b (between a and c) and g (between a and b). The symmetries place restrictions on these coordinates and angles as follows: Triclinic no restrictions Monoclinic a=g=90o Orthorhomic a=b=g=90o Tetragonal a=b=g=90o a=b Hexagonal a=b=90o g=120o a=b Rhombohedral a=b=g<120o a=b=c Cubic a=b=g=90o a=b=c Click and hold the mouse over the CHIME image, then move the mouse to rotate the Bravais lattice displayed. The origin is highlighted by a red sphere.
Hexagonal (hP) Rhombohedral (hR) [hP and hR] Cubic (cP) Cubic (cI) Cubic (cF) A crystal, which has a regularly repeating pattern of atoms, may be represented by a lattice - a set of points which have identical surroundings. Thus, for a crystal, each lattice point is surrounded by the same geometrical arrangement of atoms. Bravais lattices are named after Auguste Bravais who, in 1848, described fourteen distinct three-dimensional arrangements of lattice points. The Bravais lattices are classified by symmetry and centring, and all fourteen may be shown by clicking the buttons above. Six symmetries are defined: triclinic (a - for anorthic), monoclinic (m), orthorhombic (o), tetragonal (t), hexagonal or trigonal (h) and cubic (c). Primitive (P) and rhombohedral (R) have lattice points at corners only. Additional lattice points are required at centres of opposite unit cell faces for centred lattices (A, B, or C faces), at centres of all faces for face centred lattices (F), and at body centres for 'Innenzentrierte' lattices (I). Each Bravais lattice is defined by three unit cell coordinates (a,b and c) and by angles between these coordinates, a (between b and c), b (between a and c) and g (between a and b). The symmetries place restrictions on these coordinates and angles as follows: Triclinic no restrictions Monoclinic a=g=90o Orthorhomic a=b=g=90o Tetragonal a=b=g=90o a=b Hexagonal a=b=90o g=120o a=b Rhombohedral a=b=g<120o a=b=c Cubic a=b=g=90o a=b=c Click and hold the mouse over the CHIME image, then move the mouse to rotate the Bravais lattice displayed. The origin is highlighted by a red sphere.
Cubic (cP) Cubic (cI) Cubic (cF) A crystal, which has a regularly repeating pattern of atoms, may be represented by a lattice - a set of points which have identical surroundings. Thus, for a crystal, each lattice point is surrounded by the same geometrical arrangement of atoms. Bravais lattices are named after Auguste Bravais who, in 1848, described fourteen distinct three-dimensional arrangements of lattice points. The Bravais lattices are classified by symmetry and centring, and all fourteen may be shown by clicking the buttons above. Six symmetries are defined: triclinic (a - for anorthic), monoclinic (m), orthorhombic (o), tetragonal (t), hexagonal or trigonal (h) and cubic (c). Primitive (P) and rhombohedral (R) have lattice points at corners only. Additional lattice points are required at centres of opposite unit cell faces for centred lattices (A, B, or C faces), at centres of all faces for face centred lattices (F), and at body centres for 'Innenzentrierte' lattices (I). Each Bravais lattice is defined by three unit cell coordinates (a,b and c) and by angles between these coordinates, a (between b and c), b (between a and c) and g (between a and b). The symmetries place restrictions on these coordinates and angles as follows: Triclinic no restrictions Monoclinic a=g=90o Orthorhomic a=b=g=90o Tetragonal a=b=g=90o a=b Hexagonal a=b=90o g=120o a=b Rhombohedral a=b=g<120o a=b=c Cubic a=b=g=90o a=b=c Click and hold the mouse over the CHIME image, then move the mouse to rotate the Bravais lattice displayed. The origin is highlighted by a red sphere.
A crystal, which has a regularly repeating pattern of atoms, may be represented by a lattice - a set of points which have identical surroundings. Thus, for a crystal, each lattice point is surrounded by the same geometrical arrangement of atoms.
Bravais lattices are named after Auguste Bravais who, in 1848, described fourteen distinct three-dimensional arrangements of lattice points. The Bravais lattices are classified by symmetry and centring, and all fourteen may be shown by clicking the buttons above.
Six symmetries are defined: triclinic (a - for anorthic), monoclinic (m), orthorhombic (o), tetragonal (t), hexagonal or trigonal (h) and cubic (c). Primitive (P) and rhombohedral (R) have lattice points at corners only. Additional lattice points are required at centres of opposite unit cell faces for centred lattices (A, B, or C faces), at centres of all faces for face centred lattices (F), and at body centres for 'Innenzentrierte' lattices (I).
Each Bravais lattice is defined by three unit cell coordinates (a,b and c) and by angles between these coordinates, a (between b and c), b (between a and c) and g (between a and b). The symmetries place restrictions on these coordinates and angles as follows:
Triclinic no restrictions Monoclinic a=g=90o Orthorhomic a=b=g=90o Tetragonal a=b=g=90o a=b Hexagonal a=b=90o g=120o a=b Rhombohedral a=b=g<120o a=b=c Cubic a=b=g=90o a=b=c
Click and hold the mouse over the CHIME image, then move the mouse to rotate the Bravais lattice displayed. The origin is highlighted by a red sphere.
