Input interpretation
antimony | Bravais lattice
Result
simple trigonal
Image
Image
Unit cell relations
angle relations | α = β = γ!=90° edge relations | a = b = c unit cell volume | a b c sqrt(2 cos^3(α) - 3 cos^2(α) + 1)
Common name
rhombohedral
Description of lattice
Gram matrix | (2 | 1 | 0 1 | 2 | 1 0 | 1 | 3)
Lattice invariants
dimension | 3 determinant | 7
Lattice-packing invariants
volume | sqrt(7)≈2.64575
Quadratic form and theta series
quadratic form | 2 x^2 + 2 x y + 2 y^2 + 2 y z + 3 z^2
More properties
number of symmetries | 12
Common properties
even | integral | nonunimodular
Crystallographic properties
lattice system | rhombohedral crystal system | trigonal crystal family | hexagonal required point group symmetry | 1 3-fold rotation axis point groups | 5 space groups | 7
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
Space groups
crystal class | IUCr number | Hermann-Mauguin trigonal pyramidal | 146 | R3 rhombohedral | 148 | R3^_ trigonal trapezoidal | 155 | R32 ditrigonal pyramidal | 160 | 161 | R3m | R3c ditrigonal scalahedral | 166 | 167 | R3m^_ | R3c^_