Point Group Elements

Search elements by their Seitz name, and show their matrix representations

using LatticeTools

all_elements = Dict()
print("# Reading groups")
for i in 1:32
    print(" $i")
    psym = PointSymmetryDatabase.get(i)
    for (elname, matrep) in zip(psym.element_names, psym.matrix_representations)
        if !haskey(all_elements, elname)
            all_elements[elname] = []
        end
        push!(all_elements[elname], (matrep, psym.hermann_mauguin))
    end
end
println()

println("elements:")
for (k, v) in all_elements
    println("- element_name: $k")
    println("  matrix_representations:")
    for v2 in v
        m = [collect(x) for x in eachrow(v2[1])]
        g = v2[2]
        println("  - { matrix: $(m), group: \"$g\" }")
    end
end

# Reading groups 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
elements:
- element_name: 1
  matrix_representations:
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "1" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "-1" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "2" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "m" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "2/m" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "222" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "mm2" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "mmm" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "4" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "-4" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "4/m" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "422" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "4mm" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "-42m" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "4/mmm" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "3" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "-3" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "32" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "3m" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "-3m" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "6" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "-6" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "6/m" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "622" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "6mm" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "-62m" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "6/mmm" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "23" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "m-3" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "432" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "-43m" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "m-3m" }
- element_name: m<sub>100</sub>
  matrix_representations:
  - { matrix: [[-1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "mm2" }
  - { matrix: [[-1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "mmm" }
  - { matrix: [[-1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "4mm" }
  - { matrix: [[-1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "4/mmm" }
  - { matrix: [[-1, 1, 0], [0, 1, 0], [0, 0, 1]], group: "6mm" }
  - { matrix: [[-1, 1, 0], [0, 1, 0], [0, 0, 1]], group: "6/mmm" }
  - { matrix: [[-1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "m-3" }
  - { matrix: [[-1, 0, 0], [0, 1, 0], [0, 0, 1]], group: "m-3m" }
- element_name: m<sub>101</sub>
  matrix_representations:
  - { matrix: [[0, 0, -1], [0, 1, 0], [-1, 0, 0]], group: "-43m" }
  - { matrix: [[0, 0, -1], [0, 1, 0], [-1, 0, 0]], group: "m-3m" }
- element_name: m<sub>110</sub>
  matrix_representations:
  - { matrix: [[0, -1, 0], [-1, 0, 0], [0, 0, 1]], group: "4mm" }
  - { matrix: [[0, -1, 0], [-1, 0, 0], [0, 0, 1]], group: "-42m" }
  - { matrix: [[0, -1, 0], [-1, 0, 0], [0, 0, 1]], group: "4/mmm" }
  - { matrix: [[0, -1, 0], [-1, 0, 0], [0, 0, 1]], group: "6mm" }
  - { matrix: [[0, -1, 0], [-1, 0, 0], [0, 0, 1]], group: "6/mmm" }
  - { matrix: [[0, -1, 0], [-1, 0, 0], [0, 0, 1]], group: "-43m" }
  - { matrix: [[0, -1, 0], [-1, 0, 0], [0, 0, 1]], group: "m-3m" }
- element_name: -6<sup>+</sup><sub>001</sub>
  matrix_representations:
  - { matrix: [[-1, 1, 0], [-1, 0, 0], [0, 0, -1]], group: "-6" }
  - { matrix: [[-1, 1, 0], [-1, 0, 0], [0, 0, -1]], group: "6/m" }
  - { matrix: [[-1, 1, 0], [-1, 0, 0], [0, 0, -1]], group: "-62m" }
  - { matrix: [[-1, 1, 0], [-1, 0, 0], [0, 0, -1]], group: "6/mmm" }
- element_name: -4<sup>-</sup><sub>100</sub>
  matrix_representations:
  - { matrix: [[-1, 0, 0], [0, 0, -1], [0, 1, 0]], group: "-43m" }
  - { matrix: [[-1, 0, 0], [0, 0, -1], [0, 1, 0]], group: "m-3m" }
- element_name: 2<sub>120</sub>
  matrix_representations:
  - { matrix: [[-1, 1, 0], [0, 1, 0], [0, 0, -1]], group: "32" }
  - { matrix: [[-1, 1, 0], [0, 1, 0], [0, 0, -1]], group: "-3m" }
  - { matrix: [[-1, 1, 0], [0, 1, 0], [0, 0, -1]], group: "622" }
  - { matrix: [[-1, 1, 0], [0, 1, 0], [0, 0, -1]], group: "6/mmm" }
- element_name: 3<sup>-</sup><sub>-11-1</sub>
  matrix_representations:
  - { matrix: [[0, -1, 0], [0, 0, -1], [1, 0, 0]], group: "23" }
  - { matrix: [[0, -1, 0], [0, 0, -1], [1, 0, 0]], group: "m-3" }
  - { matrix: [[0, -1, 0], [0, 0, -1], [1, 0, 0]], group: "432" }
  - { matrix: [[0, -1, 0], [0, 0, -1], [1, 0, 0]], group: "-43m" }
  - { matrix: [[0, -1, 0], [0, 0, -1], [1, 0, 0]], group: "m-3m" }
- element_name: m<sub>011</sub>
  matrix_representations:
  - { matrix: [[1, 0, 0], [0, 0, -1], [0, -1, 0]], group: "-43m" }
  - { matrix: [[1, 0, 0], [0, 0, -1], [0, -1, 0]], group: "m-3m" }
- element_name: 2<sub>210</sub>
  matrix_representations:
  - { matrix: [[1, 0, 0], [1, -1, 0], [0, 0, -1]], group: "32" }
  - { matrix: [[1, 0, 0], [1, -1, 0], [0, 0, -1]], group: "-3m" }
  - { matrix: [[1, 0, 0], [1, -1, 0], [0, 0, -1]], group: "622" }
  - { matrix: [[1, 0, 0], [1, -1, 0], [0, 0, -1]], group: "6/mmm" }
- element_name: 3<sup>+</sup><sub>-1-11</sub>
  matrix_representations:
  - { matrix: [[0, 0, -1], [1, 0, 0], [0, -1, 0]], group: "23" }
  - { matrix: [[0, 0, -1], [1, 0, 0], [0, -1, 0]], group: "m-3" }
  - { matrix: [[0, 0, -1], [1, 0, 0], [0, -1, 0]], group: "432" }
  - { matrix: [[0, 0, -1], [1, 0, 0], [0, -1, 0]], group: "-43m" }
  - { matrix: [[0, 0, -1], [1, 0, 0], [0, -1, 0]], group: "m-3m" }
- element_name: -4<sup>-</sup><sub>010</sub>
  matrix_representations:
  - { matrix: [[0, 0, 1], [0, -1, 0], [-1, 0, 0]], group: "-43m" }
  - { matrix: [[0, 0, 1], [0, -1, 0], [-1, 0, 0]], group: "m-3m" }
- element_name: m<sub>120</sub>
  matrix_representations:
  - { matrix: [[1, -1, 0], [0, -1, 0], [0, 0, 1]], group: "3m" }
  - { matrix: [[1, -1, 0], [0, -1, 0], [0, 0, 1]], group: "-3m" }
  - { matrix: [[1, -1, 0], [0, -1, 0], [0, 0, 1]], group: "6mm" }
  - { matrix: [[1, -1, 0], [0, -1, 0], [0, 0, 1]], group: "-62m" }
  - { matrix: [[1, -1, 0], [0, -1, 0], [0, 0, 1]], group: "6/mmm" }
- element_name: 6<sup>+</sup><sub>001</sub>
  matrix_representations:
  - { matrix: [[1, -1, 0], [1, 0, 0], [0, 0, 1]], group: "6" }
  - { matrix: [[1, -1, 0], [1, 0, 0], [0, 0, 1]], group: "6/m" }
  - { matrix: [[1, -1, 0], [1, 0, 0], [0, 0, 1]], group: "622" }
  - { matrix: [[1, -1, 0], [1, 0, 0], [0, 0, 1]], group: "6mm" }
  - { matrix: [[1, -1, 0], [1, 0, 0], [0, 0, 1]], group: "6/mmm" }
- element_name: 4<sup>-</sup><sub>100</sub>
  matrix_representations:
  - { matrix: [[1, 0, 0], [0, 0, 1], [0, -1, 0]], group: "432" }
  - { matrix: [[1, 0, 0], [0, 0, 1], [0, -1, 0]], group: "m-3m" }
- element_name: -3<sup>+</sup><sub>001</sub>
  matrix_representations:
  - { matrix: [[0, 1, 0], [-1, 1, 0], [0, 0, -1]], group: "-3" }
  - { matrix: [[0, 1, 0], [-1, 1, 0], [0, 0, -1]], group: "-3m" }
  - { matrix: [[0, 1, 0], [-1, 1, 0], [0, 0, -1]], group: "6/m" }
  - { matrix: [[0, 1, 0], [-1, 1, 0], [0, 0, -1]], group: "6/mmm" }
- element_name: -4<sup>+</sup><sub>010</sub>
  matrix_representations:
  - { matrix: [[0, 0, -1], [0, -1, 0], [1, 0, 0]], group: "-43m" }
  - { matrix: [[0, 0, -1], [0, -1, 0], [1, 0, 0]], group: "m-3m" }
- element_name: 6<sup>-</sup><sub>001</sub>
  matrix_representations:
  - { matrix: [[0, 1, 0], [-1, 1, 0], [0, 0, 1]], group: "6" }
  - { matrix: [[0, 1, 0], [-1, 1, 0], [0, 0, 1]], group: "6/m" }
  - { matrix: [[0, 1, 0], [-1, 1, 0], [0, 0, 1]], group: "622" }
  - { matrix: [[0, 1, 0], [-1, 1, 0], [0, 0, 1]], group: "6mm" }
  - { matrix: [[0, 1, 0], [-1, 1, 0], [0, 0, 1]], group: "6/mmm" }
- element_name: 2<sub>110</sub>
  matrix_representations:
  - { matrix: [[0, 1, 0], [1, 0, 0], [0, 0, -1]], group: "422" }
  - { matrix: [[0, 1, 0], [1, 0, 0], [0, 0, -1]], group: "4/mmm" }
  - { matrix: [[0, 1, 0], [1, 0, 0], [0, 0, -1]], group: "622" }
  - { matrix: [[0, 1, 0], [1, 0, 0], [0, 0, -1]], group: "-62m" }
  - { matrix: [[0, 1, 0], [1, 0, 0], [0, 0, -1]], group: "6/mmm" }
  - { matrix: [[0, 1, 0], [1, 0, 0], [0, 0, -1]], group: "432" }
  - { matrix: [[0, 1, 0], [1, 0, 0], [0, 0, -1]], group: "m-3m" }
- element_name: 3<sup>+</sup><sub>001</sub>
  matrix_representations:
  - { matrix: [[0, -1, 0], [1, -1, 0], [0, 0, 1]], group: "3" }
  - { matrix: [[0, -1, 0], [1, -1, 0], [0, 0, 1]], group: "-3" }
  - { matrix: [[0, -1, 0], [1, -1, 0], [0, 0, 1]], group: "32" }
  - { matrix: [[0, -1, 0], [1, -1, 0], [0, 0, 1]], group: "3m" }
  - { matrix: [[0, -1, 0], [1, -1, 0], [0, 0, 1]], group: "-3m" }
  - { matrix: [[0, -1, 0], [1, -1, 0], [0, 0, 1]], group: "6" }
  - { matrix: [[0, -1, 0], [1, -1, 0], [0, 0, 1]], group: "-6" }
  - { matrix: [[0, -1, 0], [1, -1, 0], [0, 0, 1]], group: "6/m" }
  - { matrix: [[0, -1, 0], [1, -1, 0], [0, 0, 1]], group: "622" }
  - { matrix: [[0, -1, 0], [1, -1, 0], [0, 0, 1]], group: "6mm" }
  - { matrix: [[0, -1, 0], [1, -1, 0], [0, 0, 1]], group: "-62m" }
  - { matrix: [[0, -1, 0], [1, -1, 0], [0, 0, 1]], group: "6/mmm" }
- element_name: -3<sup>-</sup><sub>-1-11</sub>
  matrix_representations:
  - { matrix: [[0, -1, 0], [0, 0, 1], [1, 0, 0]], group: "m-3" }
  - { matrix: [[0, -1, 0], [0, 0, 1], [1, 0, 0]], group: "m-3m" }
- element_name: 2<sub>1-10</sub>
  matrix_representations:
  - { matrix: [[0, -1, 0], [-1, 0, 0], [0, 0, -1]], group: "422" }
  - { matrix: [[0, -1, 0], [-1, 0, 0], [0, 0, -1]], group: "4/mmm" }
  - { matrix: [[0, -1, 0], [-1, 0, 0], [0, 0, -1]], group: "32" }
  - { matrix: [[0, -1, 0], [-1, 0, 0], [0, 0, -1]], group: "-3m" }
  - { matrix: [[0, -1, 0], [-1, 0, 0], [0, 0, -1]], group: "622" }
  - { matrix: [[0, -1, 0], [-1, 0, 0], [0, 0, -1]], group: "6/mmm" }
  - { matrix: [[0, -1, 0], [-1, 0, 0], [0, 0, -1]], group: "432" }
  - { matrix: [[0, -1, 0], [-1, 0, 0], [0, 0, -1]], group: "m-3m" }
- element_name: 2<sub>010</sub>
  matrix_representations:
  - { matrix: [[-1, 0, 0], [0, 1, 0], [0, 0, -1]], group: "2" }
  - { matrix: [[-1, 0, 0], [0, 1, 0], [0, 0, -1]], group: "2/m" }
  - { matrix: [[-1, 0, 0], [0, 1, 0], [0, 0, -1]], group: "222" }
  - { matrix: [[-1, 0, 0], [0, 1, 0], [0, 0, -1]], group: "mmm" }
  - { matrix: [[-1, 0, 0], [0, 1, 0], [0, 0, -1]], group: "422" }
  - { matrix: [[-1, 0, 0], [0, 1, 0], [0, 0, -1]], group: "-42m" }
  - { matrix: [[-1, 0, 0], [0, 1, 0], [0, 0, -1]], group: "4/mmm" }
  - { matrix: [[-1, 0, 0], [-1, 1, 0], [0, 0, -1]], group: "622" }
  - { matrix: [[-1, 0, 0], [-1, 1, 0], [0, 0, -1]], group: "-62m" }
  - { matrix: [[-1, 0, 0], [-1, 1, 0], [0, 0, -1]], group: "6/mmm" }
  - { matrix: [[-1, 0, 0], [0, 1, 0], [0, 0, -1]], group: "23" }
  - { matrix: [[-1, 0, 0], [0, 1, 0], [0, 0, -1]], group: "m-3" }
  - { matrix: [[-1, 0, 0], [0, 1, 0], [0, 0, -1]], group: "432" }
  - { matrix: [[-1, 0, 0], [0, 1, 0], [0, 0, -1]], group: "-43m" }
  - { matrix: [[-1, 0, 0], [0, 1, 0], [0, 0, -1]], group: "m-3m" }
- element_name: 2<sub>001</sub>
  matrix_representations:
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, 1]], group: "222" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, 1]], group: "mm2" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, 1]], group: "mmm" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, 1]], group: "4" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, 1]], group: "-4" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, 1]], group: "4/m" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, 1]], group: "422" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, 1]], group: "4mm" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, 1]], group: "-42m" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, 1]], group: "4/mmm" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, 1]], group: "6" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, 1]], group: "6/m" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, 1]], group: "622" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, 1]], group: "6mm" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, 1]], group: "6/mmm" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, 1]], group: "23" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, 1]], group: "m-3" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, 1]], group: "432" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, 1]], group: "-43m" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, 1]], group: "m-3m" }
- element_name: 2<sub>011</sub>
  matrix_representations:
  - { matrix: [[-1, 0, 0], [0, 0, 1], [0, 1, 0]], group: "432" }
  - { matrix: [[-1, 0, 0], [0, 0, 1], [0, 1, 0]], group: "m-3m" }
- element_name: 2<sub>01-1</sub>
  matrix_representations:
  - { matrix: [[-1, 0, 0], [0, 0, -1], [0, -1, 0]], group: "432" }
  - { matrix: [[-1, 0, 0], [0, 0, -1], [0, -1, 0]], group: "m-3m" }
- element_name: 4<sup>-</sup><sub>001</sub>
  matrix_representations:
  - { matrix: [[0, 1, 0], [-1, 0, 0], [0, 0, 1]], group: "4" }
  - { matrix: [[0, 1, 0], [-1, 0, 0], [0, 0, 1]], group: "4/m" }
  - { matrix: [[0, 1, 0], [-1, 0, 0], [0, 0, 1]], group: "422" }
  - { matrix: [[0, 1, 0], [-1, 0, 0], [0, 0, 1]], group: "4mm" }
  - { matrix: [[0, 1, 0], [-1, 0, 0], [0, 0, 1]], group: "4/mmm" }
  - { matrix: [[0, 1, 0], [-1, 0, 0], [0, 0, 1]], group: "432" }
  - { matrix: [[0, 1, 0], [-1, 0, 0], [0, 0, 1]], group: "m-3m" }
- element_name: -3<sup>-</sup><sub>1-1-1</sub>
  matrix_representations:
  - { matrix: [[0, 1, 0], [0, 0, -1], [1, 0, 0]], group: "m-3" }
  - { matrix: [[0, 1, 0], [0, 0, -1], [1, 0, 0]], group: "m-3m" }
- element_name: 2<sub>101</sub>
  matrix_representations:
  - { matrix: [[0, 0, 1], [0, -1, 0], [1, 0, 0]], group: "432" }
  - { matrix: [[0, 0, 1], [0, -1, 0], [1, 0, 0]], group: "m-3m" }
- element_name: 2<sub>100</sub>
  matrix_representations:
  - { matrix: [[1, 0, 0], [0, -1, 0], [0, 0, -1]], group: "222" }
  - { matrix: [[1, 0, 0], [0, -1, 0], [0, 0, -1]], group: "mmm" }
  - { matrix: [[1, 0, 0], [0, -1, 0], [0, 0, -1]], group: "422" }
  - { matrix: [[1, 0, 0], [0, -1, 0], [0, 0, -1]], group: "-42m" }
  - { matrix: [[1, 0, 0], [0, -1, 0], [0, 0, -1]], group: "4/mmm" }
  - { matrix: [[1, -1, 0], [0, -1, 0], [0, 0, -1]], group: "622" }
  - { matrix: [[1, -1, 0], [0, -1, 0], [0, 0, -1]], group: "-62m" }
  - { matrix: [[1, -1, 0], [0, -1, 0], [0, 0, -1]], group: "6/mmm" }
  - { matrix: [[1, 0, 0], [0, -1, 0], [0, 0, -1]], group: "23" }
  - { matrix: [[1, 0, 0], [0, -1, 0], [0, 0, -1]], group: "m-3" }
  - { matrix: [[1, 0, 0], [0, -1, 0], [0, 0, -1]], group: "432" }
  - { matrix: [[1, 0, 0], [0, -1, 0], [0, 0, -1]], group: "-43m" }
  - { matrix: [[1, 0, 0], [0, -1, 0], [0, 0, -1]], group: "m-3m" }
- element_name: 4<sup>+</sup><sub>010</sub>
  matrix_representations:
  - { matrix: [[0, 0, 1], [0, 1, 0], [-1, 0, 0]], group: "432" }
  - { matrix: [[0, 0, 1], [0, 1, 0], [-1, 0, 0]], group: "m-3m" }
- element_name: -3<sup>+</sup><sub>-11-1</sub>
  matrix_representations:
  - { matrix: [[0, 0, -1], [1, 0, 0], [0, 1, 0]], group: "m-3" }
  - { matrix: [[0, 0, -1], [1, 0, 0], [0, 1, 0]], group: "m-3m" }
- element_name: -3<sup>+</sup><sub>-1-11</sub>
  matrix_representations:
  - { matrix: [[0, 0, 1], [-1, 0, 0], [0, 1, 0]], group: "m-3" }
  - { matrix: [[0, 0, 1], [-1, 0, 0], [0, 1, 0]], group: "m-3m" }
- element_name: -4<sup>+</sup><sub>001</sub>
  matrix_representations:
  - { matrix: [[0, 1, 0], [-1, 0, 0], [0, 0, -1]], group: "-4" }
  - { matrix: [[0, 1, 0], [-1, 0, 0], [0, 0, -1]], group: "4/m" }
  - { matrix: [[0, 1, 0], [-1, 0, 0], [0, 0, -1]], group: "-42m" }
  - { matrix: [[0, 1, 0], [-1, 0, 0], [0, 0, -1]], group: "4/mmm" }
  - { matrix: [[0, 1, 0], [-1, 0, 0], [0, 0, -1]], group: "-43m" }
  - { matrix: [[0, 1, 0], [-1, 0, 0], [0, 0, -1]], group: "m-3m" }
- element_name: 3<sup>-</sup><sub>1-1-1</sub>
  matrix_representations:
  - { matrix: [[0, -1, 0], [0, 0, 1], [-1, 0, 0]], group: "23" }
  - { matrix: [[0, -1, 0], [0, 0, 1], [-1, 0, 0]], group: "m-3" }
  - { matrix: [[0, -1, 0], [0, 0, 1], [-1, 0, 0]], group: "432" }
  - { matrix: [[0, -1, 0], [0, 0, 1], [-1, 0, 0]], group: "-43m" }
  - { matrix: [[0, -1, 0], [0, 0, 1], [-1, 0, 0]], group: "m-3m" }
- element_name: m<sub>-101</sub>
  matrix_representations:
  - { matrix: [[0, 0, 1], [0, 1, 0], [1, 0, 0]], group: "-43m" }
  - { matrix: [[0, 0, 1], [0, 1, 0], [1, 0, 0]], group: "m-3m" }
- element_name: -3<sup>+</sup><sub>1-1-1</sub>
  matrix_representations:
  - { matrix: [[0, 0, 1], [1, 0, 0], [0, -1, 0]], group: "m-3" }
  - { matrix: [[0, 0, 1], [1, 0, 0], [0, -1, 0]], group: "m-3m" }
- element_name: -3<sup>-</sup><sub>-11-1</sub>
  matrix_representations:
  - { matrix: [[0, 1, 0], [0, 0, 1], [-1, 0, 0]], group: "m-3" }
  - { matrix: [[0, 1, 0], [0, 0, 1], [-1, 0, 0]], group: "m-3m" }
- element_name: m<sub>01-1</sub>
  matrix_representations:
  - { matrix: [[1, 0, 0], [0, 0, 1], [0, 1, 0]], group: "-43m" }
  - { matrix: [[1, 0, 0], [0, 0, 1], [0, 1, 0]], group: "m-3m" }
- element_name: 3<sup>-</sup><sub>111</sub>
  matrix_representations:
  - { matrix: [[0, 1, 0], [0, 0, 1], [1, 0, 0]], group: "23" }
  - { matrix: [[0, 1, 0], [0, 0, 1], [1, 0, 0]], group: "m-3" }
  - { matrix: [[0, 1, 0], [0, 0, 1], [1, 0, 0]], group: "432" }
  - { matrix: [[0, 1, 0], [0, 0, 1], [1, 0, 0]], group: "-43m" }
  - { matrix: [[0, 1, 0], [0, 0, 1], [1, 0, 0]], group: "m-3m" }
- element_name: m<sub>001</sub>
  matrix_representations:
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, -1]], group: "mmm" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, -1]], group: "4/m" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, -1]], group: "4/mmm" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, -1]], group: "-6" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, -1]], group: "6/m" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, -1]], group: "-62m" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, -1]], group: "6/mmm" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, -1]], group: "m-3" }
  - { matrix: [[1, 0, 0], [0, 1, 0], [0, 0, -1]], group: "m-3m" }
- element_name: m<sub>210</sub>
  matrix_representations:
  - { matrix: [[-1, 0, 0], [-1, 1, 0], [0, 0, 1]], group: "3m" }
  - { matrix: [[-1, 0, 0], [-1, 1, 0], [0, 0, 1]], group: "-3m" }
  - { matrix: [[-1, 0, 0], [-1, 1, 0], [0, 0, 1]], group: "6mm" }
  - { matrix: [[-1, 0, 0], [-1, 1, 0], [0, 0, 1]], group: "-62m" }
  - { matrix: [[-1, 0, 0], [-1, 1, 0], [0, 0, 1]], group: "6/mmm" }
- element_name: -4<sup>-</sup><sub>001</sub>
  matrix_representations:
  - { matrix: [[0, -1, 0], [1, 0, 0], [0, 0, -1]], group: "-4" }
  - { matrix: [[0, -1, 0], [1, 0, 0], [0, 0, -1]], group: "4/m" }
  - { matrix: [[0, -1, 0], [1, 0, 0], [0, 0, -1]], group: "-42m" }
  - { matrix: [[0, -1, 0], [1, 0, 0], [0, 0, -1]], group: "4/mmm" }
  - { matrix: [[0, -1, 0], [1, 0, 0], [0, 0, -1]], group: "-43m" }
  - { matrix: [[0, -1, 0], [1, 0, 0], [0, 0, -1]], group: "m-3m" }
- element_name: -3<sup>+</sup><sub>111</sub>
  matrix_representations:
  - { matrix: [[0, 0, -1], [-1, 0, 0], [0, -1, 0]], group: "m-3" }
  - { matrix: [[0, 0, -1], [-1, 0, 0], [0, -1, 0]], group: "m-3m" }
- element_name: -3<sup>-</sup><sub>001</sub>
  matrix_representations:
  - { matrix: [[1, -1, 0], [1, 0, 0], [0, 0, -1]], group: "-3" }
  - { matrix: [[1, -1, 0], [1, 0, 0], [0, 0, -1]], group: "-3m" }
  - { matrix: [[1, -1, 0], [1, 0, 0], [0, 0, -1]], group: "6/m" }
  - { matrix: [[1, -1, 0], [1, 0, 0], [0, 0, -1]], group: "6/mmm" }
- element_name: 3<sup>-</sup><sub>001</sub>
  matrix_representations:
  - { matrix: [[-1, 1, 0], [-1, 0, 0], [0, 0, 1]], group: "3" }
  - { matrix: [[-1, 1, 0], [-1, 0, 0], [0, 0, 1]], group: "-3" }
  - { matrix: [[-1, 1, 0], [-1, 0, 0], [0, 0, 1]], group: "32" }
  - { matrix: [[-1, 1, 0], [-1, 0, 0], [0, 0, 1]], group: "3m" }
  - { matrix: [[-1, 1, 0], [-1, 0, 0], [0, 0, 1]], group: "-3m" }
  - { matrix: [[-1, 1, 0], [-1, 0, 0], [0, 0, 1]], group: "6" }
  - { matrix: [[-1, 1, 0], [-1, 0, 0], [0, 0, 1]], group: "-6" }
  - { matrix: [[-1, 1, 0], [-1, 0, 0], [0, 0, 1]], group: "6/m" }
  - { matrix: [[-1, 1, 0], [-1, 0, 0], [0, 0, 1]], group: "622" }
  - { matrix: [[-1, 1, 0], [-1, 0, 0], [0, 0, 1]], group: "6mm" }
  - { matrix: [[-1, 1, 0], [-1, 0, 0], [0, 0, 1]], group: "-62m" }
  - { matrix: [[-1, 1, 0], [-1, 0, 0], [0, 0, 1]], group: "6/mmm" }
- element_name: 4<sup>+</sup><sub>001</sub>
  matrix_representations:
  - { matrix: [[0, -1, 0], [1, 0, 0], [0, 0, 1]], group: "4" }
  - { matrix: [[0, -1, 0], [1, 0, 0], [0, 0, 1]], group: "4/m" }
  - { matrix: [[0, -1, 0], [1, 0, 0], [0, 0, 1]], group: "422" }
  - { matrix: [[0, -1, 0], [1, 0, 0], [0, 0, 1]], group: "4mm" }
  - { matrix: [[0, -1, 0], [1, 0, 0], [0, 0, 1]], group: "4/mmm" }
  - { matrix: [[0, -1, 0], [1, 0, 0], [0, 0, 1]], group: "432" }
  - { matrix: [[0, -1, 0], [1, 0, 0], [0, 0, 1]], group: "m-3m" }
- element_name: m<sub>1-10</sub>
  matrix_representations:
  - { matrix: [[0, 1, 0], [1, 0, 0], [0, 0, 1]], group: "4mm" }
  - { matrix: [[0, 1, 0], [1, 0, 0], [0, 0, 1]], group: "-42m" }
  - { matrix: [[0, 1, 0], [1, 0, 0], [0, 0, 1]], group: "4/mmm" }
  - { matrix: [[0, 1, 0], [1, 0, 0], [0, 0, 1]], group: "3m" }
  - { matrix: [[0, 1, 0], [1, 0, 0], [0, 0, 1]], group: "-3m" }
  - { matrix: [[0, 1, 0], [1, 0, 0], [0, 0, 1]], group: "6mm" }
  - { matrix: [[0, 1, 0], [1, 0, 0], [0, 0, 1]], group: "-62m" }
  - { matrix: [[0, 1, 0], [1, 0, 0], [0, 0, 1]], group: "6/mmm" }
  - { matrix: [[0, 1, 0], [1, 0, 0], [0, 0, 1]], group: "-43m" }
  - { matrix: [[0, 1, 0], [1, 0, 0], [0, 0, 1]], group: "m-3m" }
- element_name: -4<sup>+</sup><sub>100</sub>
  matrix_representations:
  - { matrix: [[-1, 0, 0], [0, 0, 1], [0, -1, 0]], group: "-43m" }
  - { matrix: [[-1, 0, 0], [0, 0, 1], [0, -1, 0]], group: "m-3m" }
- element_name: -1
  matrix_representations:
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, -1]], group: "-1" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, -1]], group: "2/m" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, -1]], group: "mmm" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, -1]], group: "4/m" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, -1]], group: "4/mmm" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, -1]], group: "-3" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, -1]], group: "-3m" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, -1]], group: "6/m" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, -1]], group: "6/mmm" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, -1]], group: "m-3" }
  - { matrix: [[-1, 0, 0], [0, -1, 0], [0, 0, -1]], group: "m-3m" }
- element_name: 4<sup>-</sup><sub>010</sub>
  matrix_representations:
  - { matrix: [[0, 0, -1], [0, 1, 0], [1, 0, 0]], group: "432" }
  - { matrix: [[0, 0, -1], [0, 1, 0], [1, 0, 0]], group: "m-3m" }
- element_name: 3<sup>+</sup><sub>-11-1</sub>
  matrix_representations:
  - { matrix: [[0, 0, 1], [-1, 0, 0], [0, -1, 0]], group: "23" }
  - { matrix: [[0, 0, 1], [-1, 0, 0], [0, -1, 0]], group: "m-3" }
  - { matrix: [[0, 0, 1], [-1, 0, 0], [0, -1, 0]], group: "432" }
  - { matrix: [[0, 0, 1], [-1, 0, 0], [0, -1, 0]], group: "-43m" }
  - { matrix: [[0, 0, 1], [-1, 0, 0], [0, -1, 0]], group: "m-3m" }
- element_name: m<sub>010</sub>
  matrix_representations:
  - { matrix: [[1, 0, 0], [0, -1, 0], [0, 0, 1]], group: "m" }
  - { matrix: [[1, 0, 0], [0, -1, 0], [0, 0, 1]], group: "2/m" }
  - { matrix: [[1, 0, 0], [0, -1, 0], [0, 0, 1]], group: "mm2" }
  - { matrix: [[1, 0, 0], [0, -1, 0], [0, 0, 1]], group: "mmm" }
  - { matrix: [[1, 0, 0], [0, -1, 0], [0, 0, 1]], group: "4mm" }
  - { matrix: [[1, 0, 0], [0, -1, 0], [0, 0, 1]], group: "4/mmm" }
  - { matrix: [[1, 0, 0], [1, -1, 0], [0, 0, 1]], group: "6mm" }
  - { matrix: [[1, 0, 0], [1, -1, 0], [0, 0, 1]], group: "6/mmm" }
  - { matrix: [[1, 0, 0], [0, -1, 0], [0, 0, 1]], group: "m-3" }
  - { matrix: [[1, 0, 0], [0, -1, 0], [0, 0, 1]], group: "m-3m" }
- element_name: 4<sup>+</sup><sub>100</sub>
  matrix_representations:
  - { matrix: [[1, 0, 0], [0, 0, -1], [0, 1, 0]], group: "432" }
  - { matrix: [[1, 0, 0], [0, 0, -1], [0, 1, 0]], group: "m-3m" }
- element_name: 2<sub>-101</sub>
  matrix_representations:
  - { matrix: [[0, 0, -1], [0, -1, 0], [-1, 0, 0]], group: "432" }
  - { matrix: [[0, 0, -1], [0, -1, 0], [-1, 0, 0]], group: "m-3m" }
- element_name: 3<sup>+</sup><sub>1-1-1</sub>
  matrix_representations:
  - { matrix: [[0, 0, -1], [-1, 0, 0], [0, 1, 0]], group: "23" }
  - { matrix: [[0, 0, -1], [-1, 0, 0], [0, 1, 0]], group: "m-3" }
  - { matrix: [[0, 0, -1], [-1, 0, 0], [0, 1, 0]], group: "432" }
  - { matrix: [[0, 0, -1], [-1, 0, 0], [0, 1, 0]], group: "-43m" }
  - { matrix: [[0, 0, -1], [-1, 0, 0], [0, 1, 0]], group: "m-3m" }
- element_name: -6<sup>-</sup><sub>001</sub>
  matrix_representations:
  - { matrix: [[0, -1, 0], [1, -1, 0], [0, 0, -1]], group: "-6" }
  - { matrix: [[0, -1, 0], [1, -1, 0], [0, 0, -1]], group: "6/m" }
  - { matrix: [[0, -1, 0], [1, -1, 0], [0, 0, -1]], group: "-62m" }
  - { matrix: [[0, -1, 0], [1, -1, 0], [0, 0, -1]], group: "6/mmm" }
- element_name: -3<sup>-</sup><sub>111</sub>
  matrix_representations:
  - { matrix: [[0, -1, 0], [0, 0, -1], [-1, 0, 0]], group: "m-3" }
  - { matrix: [[0, -1, 0], [0, 0, -1], [-1, 0, 0]], group: "m-3m" }
- element_name: 3<sup>-</sup><sub>-1-11</sub>
  matrix_representations:
  - { matrix: [[0, 1, 0], [0, 0, -1], [-1, 0, 0]], group: "23" }
  - { matrix: [[0, 1, 0], [0, 0, -1], [-1, 0, 0]], group: "m-3" }
  - { matrix: [[0, 1, 0], [0, 0, -1], [-1, 0, 0]], group: "432" }
  - { matrix: [[0, 1, 0], [0, 0, -1], [-1, 0, 0]], group: "-43m" }
  - { matrix: [[0, 1, 0], [0, 0, -1], [-1, 0, 0]], group: "m-3m" }
- element_name: 3<sup>+</sup><sub>111</sub>
  matrix_representations:
  - { matrix: [[0, 0, 1], [1, 0, 0], [0, 1, 0]], group: "23" }
  - { matrix: [[0, 0, 1], [1, 0, 0], [0, 1, 0]], group: "m-3" }
  - { matrix: [[0, 0, 1], [1, 0, 0], [0, 1, 0]], group: "432" }
  - { matrix: [[0, 0, 1], [1, 0, 0], [0, 1, 0]], group: "-43m" }
  - { matrix: [[0, 0, 1], [1, 0, 0], [0, 1, 0]], group: "m-3m" }

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