Input interpretation
corundum (mineral) | crystal system | ludlockite (mineral) | crystal system
Result
trigonal | triclinic
Basic properties
| trigonal | triclinic crystal families | hexagonal | triclinic required symmetries | 1 3-fold rotation axis | none Bravais lattices | 2 | 1 point groups | 5 | 2 space groups | 25 | 2
Lattice properties
| trigonal | triclinic lattice systems | rhombohedral | hexagonal | triclinic Bravais lattices | simple trigonal | simple hexagonal | simple triclinic angle relations | α = β = γ!=90° | α = 90°, γ = 120° | α!=β!=γ edge relations | a = b = c | a!=c | a!=b!=c unit cell volume | a b c sqrt(2 cos^3(α) - 3 cos^2(α) + 1) | 1/2 sqrt(3) a^2 c | a b c sqrt(2 cos(α) cos(β) cos(γ) - cos^2(α) - cos^2(β) - cos^2(γ) + 1)
Corresponding symmetry groups
| trigonal | triclinic crystal class | trigonal pyramidal | rhombohedral | trigonal trapezoidal | ditrigonal pyramidal | ditrigonal scalahedral | pedial | pinacoidal Schönflies point groups | {C_3, S_6, D_3, C_3v, D_3d} | {C_1, C_i} Hermann-Mauguin point groups | 3 | 3^_ | 32 | 3m | 3^_m | 1 | 1^_ IUCr space group number | 143 | 144 | 145 | 146 | 147 | 148 | 149 | 150 | 151 | 152 | ... (total: 25) | 1 | 2 Hermann-Mauguin space groups | P3 | P3_1 | P3_2 | R3 | P3^_ | R3^_ | P312 | P321 | P3_112 | P3_121 | ... (total: 25) | P1 | P1^_