Little Group in 3D

using LatticeTools

unitcell = makeunitcell([1.0 0.0 0.0; 0.0 1.0 0.0; 0 0 1]; SiteType=String)
addsite!(unitcell, "Ox", FractCoord([0,0,0], [0.5, 0.0, 0.0]))
addsite!(unitcell, "Oy", FractCoord([0,0,0], [0.0, 0.5, 0.0]))

2

Currently, makelattice in three-dimension is not well supported

lattice = makelattice(unitcell, [4 0 0; 0 4 0; 0 0 3], [1 0 0; 0 1 0; 0 0 1])
tsym = TranslationSymmetry(lattice.hypercube, [1 0 0; 0 1 0; 0 0 1])
psym = project(PointSymmetryDatabase.get(15), [1 0 0; 0 1 0; 0 0 1])

for idx in 1:num_irreps(tsym)
    kf = tsym.fractional_momenta[idx]
    k = lattice.unitcell.reducedreciprocallatticevectors * kf
    psym_little1 = little_symmetry(tsym, idx, psym)
    psym_little2 = LatticeTools.little_symmetry_iso(tsym, idx, psym)
    println("- irrep_index: $(idx)")
    println("  momentum: $(k)")
    println("  little_point_group1: { name: \"$(psym_little1.hermann_mauguin)\", order: $(group_order(psym_little1)) }")
    println("  little_point_group2: { name: \"$(psym_little2.hermann_mauguin)\", order: $(group_order(psym_little2)) }")
    println("  is_psym_compatible: $(iscompatible(tsym, idx, psym))")
    println("  is_psym_little1_compatible: $(iscompatible(tsym, idx, psym_little1))")
    println("  is_psym_little2_compatible: $(iscompatible(tsym, idx, psym_little2))")
end

- irrep_index: 1
  momentum: [0.0, 0.0, 0.0]
  little_point_group1: { name: "4/mmm", order: 16 }
  little_point_group2: { name: "4/mmm", order: 16 }
  is_psym_compatible: true
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 2
  momentum: [0.25, 0.0, 0.0]
  little_point_group1: { name: "mm2", order: 4 }
  little_point_group2: { name: "mm2", order: 4 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 3
  momentum: [0.5, 0.0, 0.0]
  little_point_group1: { name: "mmm", order: 8 }
  little_point_group2: { name: "mmm", order: 8 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 4
  momentum: [0.75, 0.0, 0.0]
  little_point_group1: { name: "mm2", order: 4 }
  little_point_group2: { name: "mm2", order: 4 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 5
  momentum: [0.0, 0.25, 0.0]
  little_point_group1: { name: "mm2", order: 4 }
  little_point_group2: { name: "mm2", order: 4 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 6
  momentum: [0.25, 0.25, 0.0]
  little_point_group1: { name: "mm2", order: 4 }
  little_point_group2: { name: "mm2", order: 4 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 7
  momentum: [0.5, 0.25, 0.0]
  little_point_group1: { name: "mm2", order: 4 }
  little_point_group2: { name: "mm2", order: 4 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 8
  momentum: [0.75, 0.25, 0.0]
  little_point_group1: { name: "mm2", order: 4 }
  little_point_group2: { name: "mm2", order: 4 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 9
  momentum: [0.0, 0.5, 0.0]
  little_point_group1: { name: "mmm", order: 8 }
  little_point_group2: { name: "mmm", order: 8 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 10
  momentum: [0.25, 0.5, 0.0]
  little_point_group1: { name: "mm2", order: 4 }
  little_point_group2: { name: "mm2", order: 4 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 11
  momentum: [0.5, 0.5, 0.0]
  little_point_group1: { name: "4/mmm", order: 16 }
  little_point_group2: { name: "4/mmm", order: 16 }
  is_psym_compatible: true
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 12
  momentum: [0.75, 0.5, 0.0]
  little_point_group1: { name: "mm2", order: 4 }
  little_point_group2: { name: "mm2", order: 4 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 13
  momentum: [0.0, 0.75, 0.0]
  little_point_group1: { name: "mm2", order: 4 }
  little_point_group2: { name: "mm2", order: 4 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 14
  momentum: [0.25, 0.75, 0.0]
  little_point_group1: { name: "mm2", order: 4 }
  little_point_group2: { name: "mm2", order: 4 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 15
  momentum: [0.5, 0.75, 0.0]
  little_point_group1: { name: "mm2", order: 4 }
  little_point_group2: { name: "mm2", order: 4 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 16
  momentum: [0.75, 0.75, 0.0]
  little_point_group1: { name: "mm2", order: 4 }
  little_point_group2: { name: "mm2", order: 4 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 17
  momentum: [0.0, 0.0, 0.3333333333333333]
  little_point_group1: { name: "4mm", order: 8 }
  little_point_group2: { name: "4mm", order: 8 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 18
  momentum: [0.25, 0.0, 0.3333333333333333]
  little_point_group1: { name: "m", order: 2 }
  little_point_group2: { name: "m", order: 2 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 19
  momentum: [0.5, 0.0, 0.3333333333333333]
  little_point_group1: { name: "mm2", order: 4 }
  little_point_group2: { name: "mm2", order: 4 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 20
  momentum: [0.75, 0.0, 0.3333333333333333]
  little_point_group1: { name: "m", order: 2 }
  little_point_group2: { name: "m", order: 2 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 21
  momentum: [0.0, 0.25, 0.3333333333333333]
  little_point_group1: { name: "m", order: 2 }
  little_point_group2: { name: "m", order: 2 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 22
  momentum: [0.25, 0.25, 0.3333333333333333]
  little_point_group1: { name: "m", order: 2 }
  little_point_group2: { name: "m", order: 2 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 23
  momentum: [0.5, 0.25, 0.3333333333333333]
  little_point_group1: { name: "m", order: 2 }
  little_point_group2: { name: "m", order: 2 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 24
  momentum: [0.75, 0.25, 0.3333333333333333]
  little_point_group1: { name: "m", order: 2 }
  little_point_group2: { name: "m", order: 2 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 25
  momentum: [0.0, 0.5, 0.3333333333333333]
  little_point_group1: { name: "mm2", order: 4 }
  little_point_group2: { name: "mm2", order: 4 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 26
  momentum: [0.25, 0.5, 0.3333333333333333]
  little_point_group1: { name: "m", order: 2 }
  little_point_group2: { name: "m", order: 2 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 27
  momentum: [0.5, 0.5, 0.3333333333333333]
  little_point_group1: { name: "4mm", order: 8 }
  little_point_group2: { name: "4mm", order: 8 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 28
  momentum: [0.75, 0.5, 0.3333333333333333]
  little_point_group1: { name: "m", order: 2 }
  little_point_group2: { name: "m", order: 2 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 29
  momentum: [0.0, 0.75, 0.3333333333333333]
  little_point_group1: { name: "m", order: 2 }
  little_point_group2: { name: "m", order: 2 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 30
  momentum: [0.25, 0.75, 0.3333333333333333]
  little_point_group1: { name: "m", order: 2 }
  little_point_group2: { name: "m", order: 2 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 31
  momentum: [0.5, 0.75, 0.3333333333333333]
  little_point_group1: { name: "m", order: 2 }
  little_point_group2: { name: "m", order: 2 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 32
  momentum: [0.75, 0.75, 0.3333333333333333]
  little_point_group1: { name: "m", order: 2 }
  little_point_group2: { name: "m", order: 2 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 33
  momentum: [0.0, 0.0, 0.6666666666666666]
  little_point_group1: { name: "4mm", order: 8 }
  little_point_group2: { name: "4mm", order: 8 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 34
  momentum: [0.25, 0.0, 0.6666666666666666]
  little_point_group1: { name: "m", order: 2 }
  little_point_group2: { name: "m", order: 2 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 35
  momentum: [0.5, 0.0, 0.6666666666666666]
  little_point_group1: { name: "mm2", order: 4 }
  little_point_group2: { name: "mm2", order: 4 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 36
  momentum: [0.75, 0.0, 0.6666666666666666]
  little_point_group1: { name: "m", order: 2 }
  little_point_group2: { name: "m", order: 2 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 37
  momentum: [0.0, 0.25, 0.6666666666666666]
  little_point_group1: { name: "m", order: 2 }
  little_point_group2: { name: "m", order: 2 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 38
  momentum: [0.25, 0.25, 0.6666666666666666]
  little_point_group1: { name: "m", order: 2 }
  little_point_group2: { name: "m", order: 2 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 39
  momentum: [0.5, 0.25, 0.6666666666666666]
  little_point_group1: { name: "m", order: 2 }
  little_point_group2: { name: "m", order: 2 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 40
  momentum: [0.75, 0.25, 0.6666666666666666]
  little_point_group1: { name: "m", order: 2 }
  little_point_group2: { name: "m", order: 2 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 41
  momentum: [0.0, 0.5, 0.6666666666666666]
  little_point_group1: { name: "mm2", order: 4 }
  little_point_group2: { name: "mm2", order: 4 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 42
  momentum: [0.25, 0.5, 0.6666666666666666]
  little_point_group1: { name: "m", order: 2 }
  little_point_group2: { name: "m", order: 2 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 43
  momentum: [0.5, 0.5, 0.6666666666666666]
  little_point_group1: { name: "4mm", order: 8 }
  little_point_group2: { name: "4mm", order: 8 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 44
  momentum: [0.75, 0.5, 0.6666666666666666]
  little_point_group1: { name: "m", order: 2 }
  little_point_group2: { name: "m", order: 2 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 45
  momentum: [0.0, 0.75, 0.6666666666666666]
  little_point_group1: { name: "m", order: 2 }
  little_point_group2: { name: "m", order: 2 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 46
  momentum: [0.25, 0.75, 0.6666666666666666]
  little_point_group1: { name: "m", order: 2 }
  little_point_group2: { name: "m", order: 2 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 47
  momentum: [0.5, 0.75, 0.6666666666666666]
  little_point_group1: { name: "m", order: 2 }
  little_point_group2: { name: "m", order: 2 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true
- irrep_index: 48
  momentum: [0.75, 0.75, 0.6666666666666666]
  little_point_group1: { name: "m", order: 2 }
  little_point_group2: { name: "m", order: 2 }
  is_psym_compatible: false
  is_psym_little1_compatible: true
  is_psym_little2_compatible: true

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