Input interpretation
![cadmium | Bravais lattice](../image_source/8510e0420790c1514c9c03a9d34f5d7f.png)
cadmium | Bravais lattice
Result
![simple hexagonal](../image_source/eed89470e3e11c22fd71f2b99287f756.png)
simple hexagonal
Image
![Image](../image_source/5799c5960e9d908f47e50ad41876fef6.png)
Image
Unit cell relations
![angle relations | α = 90°, γ = 120° edge relations | a!=c unit cell volume | 1/2 sqrt(3) a^2 c](../image_source/82bf7292fd62f2d6046afa487d846b57.png)
angle relations | α = 90°, γ = 120° edge relations | a!=c unit cell volume | 1/2 sqrt(3) a^2 c
Description of lattice
![Gram matrix | (1 | 0 | 0 0 | 2 | 1 0 | 1 | 2)](../image_source/6636470d7ca9900869ebc5b8e9bf6344.png)
Gram matrix | (1 | 0 | 0 0 | 2 | 1 0 | 1 | 2)
Lattice invariants
![dimension | 3 determinant | 3](../image_source/e8d6bded622ae18659810c04b1045bed.png)
dimension | 3 determinant | 3
Lattice-packing invariants
![volume | sqrt(3)≈1.73205](../image_source/f815b26c07dd92f191bde537406810cc.png)
volume | sqrt(3)≈1.73205
Quadratic form and theta series
![quadratic form | x^2 + 2 y^2 + 2 y z + 2 z^2](../image_source/5569cf39f784ed09f5ad689a331520af.png)
quadratic form | x^2 + 2 y^2 + 2 y z + 2 z^2
More properties
![number of symmetries | 24](../image_source/5b8769d1f4d98688dd269353c0b9c81c.png)
number of symmetries | 24
Common properties
![even | integral | nonunimodular](../image_source/a2e5918f5a9d2d1862f0914a92ac05a9.png)
even | integral | nonunimodular
Crystallographic properties
![lattice system | hexagonal crystal system | trigonal | hexagonal crystal family | hexagonal required point group symmetry | 1 3-fold rotation axis | 1 6-fold rotation axis point groups | 12 space groups | 45](../image_source/3c4302cc4a379de8a51ea7e72d4b0417.png)
lattice system | hexagonal crystal system | trigonal | hexagonal crystal family | hexagonal required point group symmetry | 1 3-fold rotation axis | 1 6-fold rotation axis point groups | 12 space groups | 45
Point groups
![crystal class | Schönflies | Hermann-Mauguin trigonal pyramidal | C_3 | 3 rhombohedral | S_6 | 3^_ trigonal trapezoidal | D_3 | 32 ditrigonal pyramidal | C_3v | 3m ditrigonal scalahedral | D_3d | 3^_m hexagonal pyramidal | C_6 | 6 trigonal dipyramidal | C_3h | 6^_ hexagonal dipyramidal | C_6h | 6/m hexagonal trapezoidal | D_6 | 622 dihexagonal pyramidal | C_6v | 6mm ditrigonal dipyramidal | D_3h | 6^_m2 dihexagonal dipyramidal | D_6h | 6/mmm](../image_source/78acb06b60d5ceadd541c9e6fe0c7bb3.png)
crystal class | Schönflies | Hermann-Mauguin trigonal pyramidal | C_3 | 3 rhombohedral | S_6 | 3^_ trigonal trapezoidal | D_3 | 32 ditrigonal pyramidal | C_3v | 3m ditrigonal scalahedral | D_3d | 3^_m hexagonal pyramidal | C_6 | 6 trigonal dipyramidal | C_3h | 6^_ hexagonal dipyramidal | C_6h | 6/m hexagonal trapezoidal | D_6 | 622 dihexagonal pyramidal | C_6v | 6mm ditrigonal dipyramidal | D_3h | 6^_m2 dihexagonal dipyramidal | D_6h | 6/mmm
Space groups
![crystal class | IUCr number | Hermann-Mauguin trigonal pyramidal | 143 | 144 | 145 | P3 | P31 | P32 rhombohedral | 147 | P3^_ trigonal trapezoidal | 149 | 150 | 151 | 152 | 153 | 154 | P312 | P321 | P3112 | P3121 | P3212 | P3221 ditrigonal pyramidal | 156 | 157 | 158 | 159 | P3m1 | P31m | P3c1 | P31c ditrigonal scalahedral | 162 | 163 | 164 | 165 | P31m^_ | P31c^_ | P3m1^_ | P3c1^_ hexagonal pyramidal | 168 | 169 | 170 | 171 | 172 | 173 | P6 | P61 | P65 | P62 | P64 | P63 trigonal dipyramidal | 174 | P6^_ hexagonal dipyramidal | 175 | 176 | P6/m | P63/m hexagonal trapezoidal | 177 | 178 | 179 | 180 | 181 | 182 | P622 | P6122 | P6522 | P6222 | P6422 | P6322 dihexagonal pyramidal | 183 | 184 | 185 | 186 | P6mm | P6cc | P63cm | P63mc ditrigonal dipyramidal | 187 | 188 | 189 | 190 | P6m2^_ | P6c2^_ | P62m^_ | P62c^_ dihexagonal dipyramidal | 191 | 192 | 193 | 194 | P6/mmm | P6/mcc | P63/mcm | P63/mmc](../image_source/26ee3992ddb3ee4d9a808babf2ed6939.png)
crystal class | IUCr number | Hermann-Mauguin trigonal pyramidal | 143 | 144 | 145 | P3 | P31 | P32 rhombohedral | 147 | P3^_ trigonal trapezoidal | 149 | 150 | 151 | 152 | 153 | 154 | P312 | P321 | P3112 | P3121 | P3212 | P3221 ditrigonal pyramidal | 156 | 157 | 158 | 159 | P3m1 | P31m | P3c1 | P31c ditrigonal scalahedral | 162 | 163 | 164 | 165 | P31m^_ | P31c^_ | P3m1^_ | P3c1^_ hexagonal pyramidal | 168 | 169 | 170 | 171 | 172 | 173 | P6 | P61 | P65 | P62 | P64 | P63 trigonal dipyramidal | 174 | P6^_ hexagonal dipyramidal | 175 | 176 | P6/m | P63/m hexagonal trapezoidal | 177 | 178 | 179 | 180 | 181 | 182 | P622 | P6122 | P6522 | P6222 | P6422 | P6322 dihexagonal pyramidal | 183 | 184 | 185 | 186 | P6mm | P6cc | P63cm | P63mc ditrigonal dipyramidal | 187 | 188 | 189 | 190 | P6m2^_ | P6c2^_ | P62m^_ | P62c^_ dihexagonal dipyramidal | 191 | 192 | 193 | 194 | P6/mmm | P6/mcc | P63/mcm | P63/mmc