# list of data for structure
#    cell = np.eye(3)
#    species = [1, 2, 3, 1]
#    positions = np.array([[0, 0, 0], [0.5, 0.5, 0.5],
#                          [0.1, 0.1, 0.1], [0.75, 0.75, 0.75]])
# all bonds
bond_list = {\
    (1, 1): {'count': [1, 3, 6, 3, 1, 12, 8, 3, 6, 3, 3, 3, 1],
             'bond':[0.4330127018922193, 0.82915619758885,
                     1.0, 1.0897247358851685, 1.299038105676658,
                     1.4142135623730951, 1.7320508075688772,
                     1.7853571071357126, 1.920286436967152,
                     2.0463381929681126, 2.48746859276655,
                     2.5860201081971503, 3.031088913245535]},
    (1, 2): {'count':[8, 12, 6, 1],
             'bond':[0.8660254037844386, 1.6583123951777,
                     2.179449471770337, 2.598076211353316]},
    (1, 3):{'count': [1, 3, 3, 3, 6, 2, 2, 1, 2, 3, 1],
            'bond':[0.17320508075688776, 0.9110433579144299,
                    1.1090536506409419, 1.2767145334803705,
                    1.4247806848775009, 1.5588457268119895,
                    1.5588457268119897, 1.6822603841260722,
                    1.6822603841260724, 1.797220075561143,
                    1.9052558883257653]}}

triplet_list = [
    [1, 1, 3, 0.4330127018922193, 0.17320508075688776, 0.606217782649107],
    [1, 1, 3, 0.82915619758885, 0.17320508075688776, 0.8170067319184096],
    [1, 1, 3, 0.82915619758885, 0.17320508075688776, 0.8170067319184096],
    [1, 1, 3, 0.82915619758885, 0.17320508075688776, 0.8170067319184096],
    [1, 2, 3, 0.8660254037844386, 0.17320508075688776, 1.0392304845413265],
    [1, 2, 3, 0.8660254037844386, 0.17320508075688776, 0.938083151964686],
    [1, 2, 3, 0.8660254037844386, 0.17320508075688776, 0.938083151964686],
    [1, 2, 3, 0.8660254037844386, 0.17320508075688776, 0.8246211251235321],
    [1, 2, 3, 0.8660254037844386, 0.17320508075688776, 0.938083151964686],
    [1, 2, 3, 0.8660254037844386, 0.17320508075688776, 0.8246211251235321],
    [1, 2, 3, 0.8660254037844386, 0.17320508075688776, 0.8246211251235321],
    [1, 2, 3, 0.8660254037844386, 0.17320508075688776, 0.692820323027551],
    [1, 3, 3, 0.9110433579144299, 0.17320508075688776, 1.0],
    [1, 3, 3, 0.9110433579144299, 0.17320508075688776, 1.0],
    [1, 3, 3, 0.9110433579144299, 0.17320508075688776, 1.0],
    [1, 1, 1, 0.82915619758885, 0.4330127018922193, 1.0],
    [1, 1, 1, 0.82915619758885, 0.4330127018922193, 1.0],
    [1, 1, 1, 0.82915619758885, 0.4330127018922193, 1.0],
    [1, 2, 1, 0.8660254037844386, 0.4330127018922193, 0.4330127018922193],
    [1, 2, 1, 0.8660254037844386, 0.4330127018922193, 0.82915619758885],
    [1, 2, 1, 0.8660254037844386, 0.4330127018922193, 0.82915619758885],
    [1, 2, 1, 0.8660254037844386, 0.4330127018922193, 1.0897247358851685],
    [1, 2, 1, 0.8660254037844386, 0.4330127018922193, 0.82915619758885],
    [1, 2, 1, 0.8660254037844386, 0.4330127018922193, 1.0897247358851685],
    [1, 2, 1, 0.8660254037844386, 0.4330127018922193, 1.0897247358851685],
    [1, 2, 1, 0.8660254037844386, 0.4330127018922193, 1.299038105676658],
    [1, 3, 1, 0.9110433579144299, 0.4330127018922193, 0.8170067319184096],
    [1, 3, 1, 0.9110433579144299, 0.4330127018922193, 0.8170067319184096],
    [1, 3, 1, 0.9110433579144299, 0.4330127018922193, 0.8170067319184096],
    [1, 1, 1, 0.82915619758885, 0.82915619758885, 1.4142135623730951],
    [1, 1, 1, 0.82915619758885, 0.82915619758885, 1.4142135623730951],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.299038105676658],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 0.4330127018922193],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.479019945774904],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 0.82915619758885],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.479019945774904],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 0.82915619758885],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.6393596310755],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.0897247358851685],
    [1, 3, 1, 0.9110433579144299, 0.82915619758885, 0.9836157786453001],
    [1, 3, 1, 0.9110433579144299, 0.82915619758885, 0.9836157786453001],
    [1, 3, 1, 0.9110433579144299, 0.82915619758885, 1.7226433176952214],
    [1, 1, 1, 0.82915619758885, 0.82915619758885, 1.4142135623730951],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.299038105676658],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.479019945774904],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 0.4330127018922193],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 0.82915619758885],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.479019945774904],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.6393596310755],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 0.82915619758885],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.0897247358851685],
    [1, 3, 1, 0.9110433579144299, 0.82915619758885, 0.9836157786453001],
    [1, 3, 1, 0.9110433579144299, 0.82915619758885, 1.7226433176952214],
    [1, 3, 1, 0.9110433579144299, 0.82915619758885, 0.9836157786453001],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.299038105676658],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.479019945774904],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.479019945774904],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.6393596310755],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 0.4330127018922193],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 0.82915619758885],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 0.82915619758885],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.0897247358851685],
    [1, 3, 1, 0.9110433579144299, 0.82915619758885, 1.7226433176952214],
    [1, 3, 1, 0.9110433579144299, 0.82915619758885, 0.9836157786453001],
    [1, 3, 1, 0.9110433579144299, 0.82915619758885, 0.9836157786453001],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.0],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.0],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.4142135623730951],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.0],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.4142135623730951],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.4142135623730951],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.7320508075688772],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 0.938083151964686],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 0.938083151964686],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 0.938083151964686],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.4142135623730951],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.0],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.4142135623730951],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.0],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.7320508075688772],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.4142135623730951],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 0.8246211251235321],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 0.8246211251235321],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 1.63707055437449],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.0],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.4142135623730951],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.7320508075688772],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.0],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.4142135623730951],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 0.8246211251235321],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 1.63707055437449],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 0.8246211251235321],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.7320508075688772],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.4142135623730951],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.4142135623730951],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.0],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 0.692820323027551],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 1.5748015748023623],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 1.574801574802362],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.0],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.0],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.4142135623730951],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 1.63707055437449],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 0.8246211251235321],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 0.8246211251235321],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.4142135623730951],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.0],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 1.5748015748023623],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 0.692820323027551],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 1.574801574802362],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.0],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 1.574801574802362],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 1.574801574802362],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 0.692820323027551],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 1.5099668870541498],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 1.5099668870541498],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 1.5099668870541498],
    [1, 3, 3, 0.9110433579144299, 0.9110433579144299, 1.4142135623730951],
    [1, 3, 3, 0.9110433579144299, 0.9110433579144299, 1.4142135623730951],
    [1, 3, 3, 0.9110433579144299, 0.9110433579144299, 1.4142135623730951]]


    [1, 1, 3, 0.4330127018922193, 0.17320508075688776, 0.606217782649107],
    [1, 2, 3, 0.8660254037844386, 0.17320508075688776, 1.0392304845413265],
    [1, 2, 3, 0.8660254037844386, 0.17320508075688776, 0.938083151964686],
    [1, 2, 3, 0.8660254037844386, 0.17320508075688776, 0.938083151964686],
    [1, 2, 3, 0.8660254037844386, 0.17320508075688776, 0.8246211251235321],
    [1, 2, 3, 0.8660254037844386, 0.17320508075688776, 0.938083151964686],
    [1, 2, 3, 0.8660254037844386, 0.17320508075688776, 0.8246211251235321],
    [1, 2, 3, 0.8660254037844386, 0.17320508075688776, 0.8246211251235321],
    [1, 2, 3, 0.8660254037844386, 0.17320508075688776, 0.692820323027551],
    [1, 3, 3, 0.9110433579144299, 0.17320508075688776, 1.0],
    [1, 3, 3, 0.9110433579144299, 0.17320508075688776, 1.0],
    [1, 3, 3, 0.9110433579144299, 0.17320508075688776, 1.0],
    [1, 2, 1, 0.8660254037844386, 0.4330127018922193, 0.4330127018922193],
    [1, 2, 1, 0.8660254037844386, 0.4330127018922193, 0.82915619758885],
    [1, 2, 1, 0.8660254037844386, 0.4330127018922193, 0.82915619758885],
    [1, 2, 1, 0.8660254037844386, 0.4330127018922193, 1.0897247358851685],
    [1, 2, 1, 0.8660254037844386, 0.4330127018922193, 0.82915619758885],
    [1, 2, 1, 0.8660254037844386, 0.4330127018922193, 1.0897247358851685],
    [1, 2, 1, 0.8660254037844386, 0.4330127018922193, 1.0897247358851685],
    [1, 2, 1, 0.8660254037844386, 0.4330127018922193, 1.299038105676658],
    [1, 3, 1, 0.9110433579144299, 0.4330127018922193, 0.8170067319184096],
    [1, 3, 1, 0.9110433579144299, 0.4330127018922193, 0.8170067319184096],
    [1, 3, 1, 0.9110433579144299, 0.4330127018922193, 0.8170067319184096],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.299038105676658],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 0.4330127018922193],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.479019945774904],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 0.82915619758885],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.479019945774904],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 0.82915619758885],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.6393596310755],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.0897247358851685],
    [1, 3, 1, 0.9110433579144299, 0.82915619758885, 0.9836157786453001],
    [1, 3, 1, 0.9110433579144299, 0.82915619758885, 0.9836157786453001],
    [1, 3, 1, 0.9110433579144299, 0.82915619758885, 1.7226433176952214],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.299038105676658],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.479019945774904],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 0.4330127018922193],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 0.82915619758885],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.479019945774904],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.6393596310755],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 0.82915619758885],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.0897247358851685],
    [1, 3, 1, 0.9110433579144299, 0.82915619758885, 0.9836157786453001],
    [1, 3, 1, 0.9110433579144299, 0.82915619758885, 1.7226433176952214],
    [1, 3, 1, 0.9110433579144299, 0.82915619758885, 0.9836157786453001],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.299038105676658],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.479019945774904],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.479019945774904],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.6393596310755],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 0.4330127018922193],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 0.82915619758885],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 0.82915619758885],
    [1, 2, 1, 0.8660254037844386, 0.82915619758885, 1.0897247358851685],
    [1, 3, 1, 0.9110433579144299, 0.82915619758885, 1.7226433176952214],
    [1, 3, 1, 0.9110433579144299, 0.82915619758885, 0.9836157786453001],
    [1, 3, 1, 0.9110433579144299, 0.82915619758885, 0.9836157786453001],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.0],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.0],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.4142135623730951],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.0],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.4142135623730951],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.4142135623730951],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.7320508075688772],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 0.938083151964686],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 0.938083151964686],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 0.938083151964686],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.4142135623730951],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.0],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.4142135623730951],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.0],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.7320508075688772],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.4142135623730951],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 0.8246211251235321],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 0.8246211251235321],
    [1, 3, 2, 0.9110433579144299, 0.8660254037844386, 1.63707055437449],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.0],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.4142135623730951],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.7320508075688772],
    [1, 2, 2, 0.8660254037844386, 0.8660254037844386, 1.0],
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