Input interpretation
diamond (mineral) | crystal system | quartz (mineral) | crystal system
Result
cubic | trigonal
Basic properties
| cubic | trigonal crystal families | cubic | hexagonal required symmetries | 4 3-fold rotation axes | 1 3-fold rotation axis Bravais lattices | 3 | 2 point groups | 5 | 5 space groups | 36 | 25
Lattice properties
| cubic | trigonal lattice systems | cubic | rhombohedral | hexagonal Bravais lattices | simple cubic | body-centered cubic | face-centered cubic | simple trigonal | simple hexagonal angle relations | α = β = γ = 90° | α = β = γ!=90° | α = 90°, γ = 120° edge relations | a = b = c | a = b = c | a!=c unit cell volume | a b c | a b c sqrt(2 cos^3(α) - 3 cos^2(α) + 1) | 1/2 sqrt(3) a^2 c
Corresponding symmetry groups
| cubic | trigonal crystal class | tetartoidal | diploidal | gyroidal | tetrahedral | hexoctahedral | trigonal pyramidal | rhombohedral | trigonal trapezoidal | ditrigonal pyramidal | ditrigonal scalahedral Schönflies point groups | {T, T_h, O, T_d, O_h} | {C_3, S_6, D_3, C_3v, D_3d} Hermann-Mauguin point groups | 23 | m3^_ | 432 | 4^_3m | m3^_m | 3 | 3^_ | 32 | 3m | 3^_m IUCr space group number | 195 | 196 | 197 | 198 | 199 | 200 | 201 | 202 | 203 | 204 | ... (total: 36) | 143 | 144 | 145 | 146 | 147 | 148 | 149 | 150 | 151 | 152 | ... (total: 25) Hermann-Mauguin space groups | P23 | F23 | I23 | P2_13 | I2_13 | Pm3^_ | Pn3^_ | Fm3^_ | Fd3^_ | Im3^_ | ... (total: 36) | P3 | P3_1 | P3_2 | R3 | P3^_ | R3^_ | P312 | P321 | P3_112 | P3_121 | ... (total: 25)