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  • # ##### BEGIN GPL LICENSE BLOCK #####
    #
    #  This program is free software; you can redistribute it and/or
    #  modify it under the terms of the GNU General Public License
    #  as published by the Free Software Foundation; either version 2
    #  of the License, or (at your option) any later version.
    #
    #  This program is distributed in the hope that it will be useful,
    #  but WITHOUT ANY WARRANTY; without even the implied warranty of
    #  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    #  GNU General Public License for more details.
    #
    #  You should have received a copy of the GNU General Public License
    #  along with this program; if not, write to the Free Software Foundation,
    #  Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
    #
    # ##### END GPL LICENSE BLOCK #####
    
    import bpy
    import io
    import math
    import os
    import copy
    from math import pi, cos, sin, tan, sqrt
    from mathutils import Vector, Matrix
    from copy import copy
    
    # -----------------------------------------------------------------------------
    #                                                  Atom, stick and element data
    
    
    # This is a list that contains some data of all possible elements. The structure
    # is as follows:
    #
    # 1, "Hydrogen", "H", [0.0,0.0,1.0], 0.32, 0.32, 0.32 , -1 , 1.54   means
    #
    # No., name, short name, color, radius (used), radius (covalent), radius (atomic),
    #
    # charge state 1, radius (ionic) 1, charge state 2, radius (ionic) 2, ... all
    # charge states for any atom are listed, if existing.
    # The list is fixed and cannot be changed ... (see below)
    
    ATOM_CLUSTER_ELEMENTS_DEFAULT = (
    ( 1,      "Hydrogen",        "H", (  1.0,   1.0,   1.0), 0.32, 0.32, 0.79 , -1 , 1.54 ),
    ( 2,        "Helium",       "He", ( 0.85,   1.0,   1.0), 0.93, 0.93, 0.49 ),
    ( 3,       "Lithium",       "Li", (  0.8,  0.50,   1.0), 1.23, 1.23, 2.05 ,  1 , 0.68 ),
    ( 4,     "Beryllium",       "Be", ( 0.76,   1.0,   0.0), 0.90, 0.90, 1.40 ,  1 , 0.44 ,  2 , 0.35 ),
    ( 5,         "Boron",        "B", (  1.0,  0.70,  0.70), 0.82, 0.82, 1.17 ,  1 , 0.35 ,  3 , 0.23 ),
    ( 6,        "Carbon",        "C", ( 0.56,  0.56,  0.56), 0.77, 0.77, 0.91 , -4 , 2.60 ,  4 , 0.16 ),
    ( 7,      "Nitrogen",        "N", ( 0.18,  0.31,  0.97), 0.75, 0.75, 0.75 , -3 , 1.71 ,  1 , 0.25 ,  3 , 0.16 ,  5 , 0.13 ),
    ( 8,        "Oxygen",        "O", (  1.0,  0.05,  0.05), 0.73, 0.73, 0.65 , -2 , 1.32 , -1 , 1.76 ,  1 , 0.22 ,  6 , 0.09 ),
    ( 9,      "Fluorine",        "F", ( 0.56,  0.87,  0.31), 0.72, 0.72, 0.57 , -1 , 1.33 ,  7 , 0.08 ),
    (10,          "Neon",       "Ne", ( 0.70,  0.89,  0.96), 0.71, 0.71, 0.51 ,  1 , 1.12 ),
    (11,        "Sodium",       "Na", ( 0.67,  0.36,  0.94), 1.54, 1.54, 2.23 ,  1 , 0.97 ),
    (12,     "Magnesium",       "Mg", ( 0.54,   1.0,   0.0), 1.36, 1.36, 1.72 ,  1 , 0.82 ,  2 , 0.66 ),
    (13,     "Aluminium",       "Al", ( 0.74,  0.65,  0.65), 1.18, 1.18, 1.82 ,  3 , 0.51 ),
    (14,       "Silicon",       "Si", ( 0.94,  0.78,  0.62), 1.11, 1.11, 1.46 , -4 , 2.71 , -1 , 3.84 ,  1 , 0.65 ,  4 , 0.42 ),
    (15,    "Phosphorus",        "P", (  1.0,  0.50,   0.0), 1.06, 1.06, 1.23 , -3 , 2.12 ,  3 , 0.44 ,  5 , 0.35 ),
    (16,        "Sulfur",        "S", (  1.0,   1.0,  0.18), 1.02, 1.02, 1.09 , -2 , 1.84 ,  2 , 2.19 ,  4 , 0.37 ,  6 , 0.30 ),
    (17,      "Chlorine",       "Cl", ( 0.12,  0.94,  0.12), 0.99, 0.99, 0.97 , -1 , 1.81 ,  5 , 0.34 ,  7 , 0.27 ),
    (18,         "Argon",       "Ar", ( 0.50,  0.81,  0.89), 0.98, 0.98, 0.88 ,  1 , 1.54 ),
    (19,     "Potassium",        "K", ( 0.56,  0.25,  0.83), 2.03, 2.03, 2.77 ,  1 , 0.81 ),
    (20,       "Calcium",       "Ca", ( 0.23,   1.0,   0.0), 1.74, 1.74, 2.23 ,  1 , 1.18 ,  2 , 0.99 ),
    (21,      "Scandium",       "Sc", ( 0.90,  0.90,  0.90), 1.44, 1.44, 2.09 ,  3 , 0.73 ),
    (22,      "Titanium",       "Ti", ( 0.74,  0.76,  0.78), 1.32, 1.32, 2.00 ,  1 , 0.96 ,  2 , 0.94 ,  3 , 0.76 ,  4 , 0.68 ),
    (23,      "Vanadium",        "V", ( 0.65,  0.65,  0.67), 1.22, 1.22, 1.92 ,  2 , 0.88 ,  3 , 0.74 ,  4 , 0.63 ,  5 , 0.59 ),
    (24,      "Chromium",       "Cr", ( 0.54,   0.6,  0.78), 1.18, 1.18, 1.85 ,  1 , 0.81 ,  2 , 0.89 ,  3 , 0.63 ,  6 , 0.52 ),
    (25,     "Manganese",       "Mn", ( 0.61,  0.47,  0.78), 1.17, 1.17, 1.79 ,  2 , 0.80 ,  3 , 0.66 ,  4 , 0.60 ,  7 , 0.46 ),
    (26,          "Iron",       "Fe", ( 0.87,   0.4,   0.2), 1.17, 1.17, 1.72 ,  2 , 0.74 ,  3 , 0.64 ),
    (27,        "Cobalt",       "Co", ( 0.94,  0.56,  0.62), 1.16, 1.16, 1.67 ,  2 , 0.72 ,  3 , 0.63 ),
    (28,        "Nickel",       "Ni", ( 0.31,  0.81,  0.31), 1.15, 1.15, 1.62 ,  2 , 0.69 ),
    (29,        "Copper",       "Cu", ( 0.78,  0.50,   0.2), 1.17, 1.17, 1.57 ,  1 , 0.96 ,  2 , 0.72 ),
    (30,          "Zinc",       "Zn", ( 0.49,  0.50,  0.69), 1.25, 1.25, 1.53 ,  1 , 0.88 ,  2 , 0.74 ),
    (31,       "Gallium",       "Ga", ( 0.76,  0.56,  0.56), 1.26, 1.26, 1.81 ,  1 , 0.81 ,  3 , 0.62 ),
    (32,     "Germanium",       "Ge", (  0.4,  0.56,  0.56), 1.22, 1.22, 1.52 , -4 , 2.72 ,  2 , 0.73 ,  4 , 0.53 ),
    (33,       "Arsenic",       "As", ( 0.74,  0.50,  0.89), 1.20, 1.20, 1.33 , -3 , 2.22 ,  3 , 0.58 ,  5 , 0.46 ),
    (34,      "Selenium",       "Se", (  1.0,  0.63,   0.0), 1.16, 1.16, 1.22 , -2 , 1.91 , -1 , 2.32 ,  1 , 0.66 ,  4 , 0.50 ,  6 , 0.42 ),
    (35,       "Bromine",       "Br", ( 0.65,  0.16,  0.16), 1.14, 1.14, 1.12 , -1 , 1.96 ,  5 , 0.47 ,  7 , 0.39 ),
    (36,       "Krypton",       "Kr", ( 0.36,  0.72,  0.81), 1.31, 1.31, 1.24 ),
    (37,      "Rubidium",       "Rb", ( 0.43,  0.18,  0.69), 2.16, 2.16, 2.98 ,  1 , 1.47 ),
    (38,     "Strontium",       "Sr", (  0.0,   1.0,   0.0), 1.91, 1.91, 2.45 ,  2 , 1.12 ),
    (39,       "Yttrium",        "Y", ( 0.58,   1.0,   1.0), 1.62, 1.62, 2.27 ,  3 , 0.89 ),
    (40,     "Zirconium",       "Zr", ( 0.58,  0.87,  0.87), 1.45, 1.45, 2.16 ,  1 , 1.09 ,  4 , 0.79 ),
    (41,       "Niobium",       "Nb", ( 0.45,  0.76,  0.78), 1.34, 1.34, 2.08 ,  1 , 1.00 ,  4 , 0.74 ,  5 , 0.69 ),
    (42,    "Molybdenum",       "Mo", ( 0.32,  0.70,  0.70), 1.30, 1.30, 2.01 ,  1 , 0.93 ,  4 , 0.70 ,  6 , 0.62 ),
    (43,    "Technetium",       "Tc", ( 0.23,  0.61,  0.61), 1.27, 1.27, 1.95 ,  7 , 0.97 ),
    (44,     "Ruthenium",       "Ru", ( 0.14,  0.56,  0.56), 1.25, 1.25, 1.89 ,  4 , 0.67 ),
    (45,       "Rhodium",       "Rh", ( 0.03,  0.49,  0.54), 1.25, 1.25, 1.83 ,  3 , 0.68 ),
    (46,     "Palladium",       "Pd", (  0.0,  0.41,  0.52), 1.28, 1.28, 1.79 ,  2 , 0.80 ,  4 , 0.65 ),
    (47,        "Silver",       "Ag", ( 0.75,  0.75,  0.75), 1.34, 1.34, 1.75 ,  1 , 1.26 ,  2 , 0.89 ),
    (48,       "Cadmium",       "Cd", (  1.0,  0.85,  0.56), 1.48, 1.48, 1.71 ,  1 , 1.14 ,  2 , 0.97 ),
    (49,        "Indium",       "In", ( 0.65,  0.45,  0.45), 1.44, 1.44, 2.00 ,  3 , 0.81 ),
    (50,           "Tin",       "Sn", (  0.4,  0.50,  0.50), 1.41, 1.41, 1.72 , -4 , 2.94 , -1 , 3.70 ,  2 , 0.93 ,  4 , 0.71 ),
    (51,      "Antimony",       "Sb", ( 0.61,  0.38,  0.70), 1.40, 1.40, 1.53 , -3 , 2.45 ,  3 , 0.76 ,  5 , 0.62 ),
    (52,     "Tellurium",       "Te", ( 0.83,  0.47,   0.0), 1.36, 1.36, 1.42 , -2 , 2.11 , -1 , 2.50 ,  1 , 0.82 ,  4 , 0.70 ,  6 , 0.56 ),
    (53,        "Iodine",        "I", ( 0.58,   0.0,  0.58), 1.33, 1.33, 1.32 , -1 , 2.20 ,  5 , 0.62 ,  7 , 0.50 ),
    (54,         "Xenon",       "Xe", ( 0.25,  0.61,  0.69), 1.31, 1.31, 1.24 ),
    (55,       "Caesium",       "Cs", ( 0.34,  0.09,  0.56), 2.35, 2.35, 3.35 ,  1 , 1.67 ),
    (56,        "Barium",       "Ba", (  0.0,  0.78,   0.0), 1.98, 1.98, 2.78 ,  1 , 1.53 ,  2 , 1.34 ),
    (57,     "Lanthanum",       "La", ( 0.43,  0.83,   1.0), 1.69, 1.69, 2.74 ,  1 , 1.39 ,  3 , 1.06 ),
    (58,        "Cerium",       "Ce", (  1.0,   1.0,  0.78), 1.65, 1.65, 2.70 ,  1 , 1.27 ,  3 , 1.03 ,  4 , 0.92 ),
    (59,  "Praseodymium",       "Pr", ( 0.85,   1.0,  0.78), 1.65, 1.65, 2.67 ,  3 , 1.01 ,  4 , 0.90 ),
    (60,     "Neodymium",       "Nd", ( 0.78,   1.0,  0.78), 1.64, 1.64, 2.64 ,  3 , 0.99 ),
    (61,    "Promethium",       "Pm", ( 0.63,   1.0,  0.78), 1.63, 1.63, 2.62 ,  3 , 0.97 ),
    (62,      "Samarium",       "Sm", ( 0.56,   1.0,  0.78), 1.62, 1.62, 2.59 ,  3 , 0.96 ),
    (63,      "Europium",       "Eu", ( 0.38,   1.0,  0.78), 1.85, 1.85, 2.56 ,  2 , 1.09 ,  3 , 0.95 ),
    (64,    "Gadolinium",       "Gd", ( 0.27,   1.0,  0.78), 1.61, 1.61, 2.54 ,  3 , 0.93 ),
    (65,       "Terbium",       "Tb", ( 0.18,   1.0,  0.78), 1.59, 1.59, 2.51 ,  3 , 0.92 ,  4 , 0.84 ),
    (66,    "Dysprosium",       "Dy", ( 0.12,   1.0,  0.78), 1.59, 1.59, 2.49 ,  3 , 0.90 ),
    (67,       "Holmium",       "Ho", (  0.0,   1.0,  0.61), 1.58, 1.58, 2.47 ,  3 , 0.89 ),
    (68,        "Erbium",       "Er", (  0.0,  0.90,  0.45), 1.57, 1.57, 2.45 ,  3 , 0.88 ),
    (69,       "Thulium",       "Tm", (  0.0,  0.83,  0.32), 1.56, 1.56, 2.42 ,  3 , 0.87 ),
    (70,     "Ytterbium",       "Yb", (  0.0,  0.74,  0.21), 1.74, 1.74, 2.40 ,  2 , 0.93 ,  3 , 0.85 ),
    (71,      "Lutetium",       "Lu", (  0.0,  0.67,  0.14), 1.56, 1.56, 2.25 ,  3 , 0.85 ),
    (72,       "Hafnium",       "Hf", ( 0.30,  0.76,   1.0), 1.44, 1.44, 2.16 ,  4 , 0.78 ),
    (73,      "Tantalum",       "Ta", ( 0.30,  0.65,   1.0), 1.34, 1.34, 2.09 ,  5 , 0.68 ),
    (74,      "Tungsten",        "W", ( 0.12,  0.58,  0.83), 1.30, 1.30, 2.02 ,  4 , 0.70 ,  6 , 0.62 ),
    (75,       "Rhenium",       "Re", ( 0.14,  0.49,  0.67), 1.28, 1.28, 1.97 ,  4 , 0.72 ,  7 , 0.56 ),
    (76,        "Osmium",       "Os", ( 0.14,   0.4,  0.58), 1.26, 1.26, 1.92 ,  4 , 0.88 ,  6 , 0.69 ),
    (77,       "Iridium",       "Ir", ( 0.09,  0.32,  0.52), 1.27, 1.27, 1.87 ,  4 , 0.68 ),
    (78,     "Platinium",       "Pt", ( 0.81,  0.81,  0.87), 1.30, 1.30, 1.83 ,  2 , 0.80 ,  4 , 0.65 ),
    (79,          "Gold",       "Au", (  1.0,  0.81,  0.13), 1.34, 1.34, 1.79 ,  1 , 1.37 ,  3 , 0.85 ),
    (80,       "Mercury",       "Hg", ( 0.72,  0.72,  0.81), 1.49, 1.49, 1.76 ,  1 , 1.27 ,  2 , 1.10 ),
    (81,      "Thallium",       "Tl", ( 0.65,  0.32,  0.30), 1.48, 1.48, 2.08 ,  1 , 1.47 ,  3 , 0.95 ),
    (82,          "Lead",       "Pb", ( 0.34,  0.34,  0.38), 1.47, 1.47, 1.81 ,  2 , 1.20 ,  4 , 0.84 ),
    (83,       "Bismuth",       "Bi", ( 0.61,  0.30,  0.70), 1.46, 1.46, 1.63 ,  1 , 0.98 ,  3 , 0.96 ,  5 , 0.74 ),
    (84,      "Polonium",       "Po", ( 0.67,  0.36,   0.0), 1.46, 1.46, 1.53 ,  6 , 0.67 ),
    (85,      "Astatine",       "At", ( 0.45,  0.30,  0.27), 1.45, 1.45, 1.43 , -3 , 2.22 ,  3 , 0.85 ,  5 , 0.46 ),
    (86,         "Radon",       "Rn", ( 0.25,  0.50,  0.58), 1.00, 1.00, 1.34 ),
    (87,      "Francium",       "Fr", ( 0.25,   0.0,   0.4), 1.00, 1.00, 1.00 ,  1 , 1.80 ),
    (88,        "Radium",       "Ra", (  0.0,  0.49,   0.0), 1.00, 1.00, 1.00 ,  2 , 1.43 ),
    (89,      "Actinium",       "Ac", ( 0.43,  0.67,  0.98), 1.00, 1.00, 1.00 ,  3 , 1.18 ),
    (90,       "Thorium",       "Th", (  0.0,  0.72,   1.0), 1.65, 1.65, 1.00 ,  4 , 1.02 ),
    (91,  "Protactinium",       "Pa", (  0.0,  0.63,   1.0), 1.00, 1.00, 1.00 ,  3 , 1.13 ,  4 , 0.98 ,  5 , 0.89 ),
    (92,       "Uranium",        "U", (  0.0,  0.56,   1.0), 1.42, 1.42, 1.00 ,  4 , 0.97 ,  6 , 0.80 ),
    (93,     "Neptunium",       "Np", (  0.0,  0.50,   1.0), 1.00, 1.00, 1.00 ,  3 , 1.10 ,  4 , 0.95 ,  7 , 0.71 ),
    (94,     "Plutonium",       "Pu", (  0.0,  0.41,   1.0), 1.00, 1.00, 1.00 ,  3 , 1.08 ,  4 , 0.93 ),
    (95,     "Americium",       "Am", ( 0.32,  0.36,  0.94), 1.00, 1.00, 1.00 ,  3 , 1.07 ,  4 , 0.92 ),
    (96,        "Curium",       "Cm", ( 0.47,  0.36,  0.89), 1.00, 1.00, 1.00 ),
    (97,     "Berkelium",       "Bk", ( 0.54,  0.30,  0.89), 1.00, 1.00, 1.00 ),
    (98,   "Californium",       "Cf", ( 0.63,  0.21,  0.83), 1.00, 1.00, 1.00 ),
    (99,   "Einsteinium",       "Es", ( 0.70,  0.12,  0.83), 1.00, 1.00, 1.00 ),
    (100,       "Fermium",       "Fm", ( 0.70,  0.12,  0.72), 1.00, 1.00, 1.00 ),
    (101,   "Mendelevium",       "Md", ( 0.70,  0.05,  0.65), 1.00, 1.00, 1.00 ),
    (102,      "Nobelium",       "No", ( 0.74,  0.05,  0.52), 1.00, 1.00, 1.00 ),
    (103,    "Lawrencium",       "Lr", ( 0.78,   0.0,   0.4), 1.00, 1.00, 1.00 ),
    (104,       "Vacancy",      "Vac", (  0.5,   0.5,   0.5), 1.00, 1.00, 1.00),
    (105,       "Default",  "Default", (  1.0,   1.0,   1.0), 1.00, 1.00, 1.00),
    (106,         "Stick",    "Stick", (  0.5,   0.5,   0.5), 1.00, 1.00, 1.00),
    )
    
    # This list here contains all data of the elements and will be used during
    # runtime. It is a list of classes.
    # During executing Atomic Blender, the list will be initialized with the fixed
    # data from above via the class structure below (CLASS_atom_pdb_Elements). We
    # have then one fixed list (above), which will never be changed, and a list of
    # classes with same data. The latter can be modified via loading a separate
    # custom data file.
    ATOM_CLUSTER_ELEMENTS = []
    ATOM_CLUSTER_ALL_ATOMS = []
    
    # This is the class, which stores the properties for one element.
    class CLASS_atom_cluster_Elements(object):
        __slots__ = ('number', 'name', 'short_name', 'color', 'radii', 'radii_ionic')
        def __init__(self, number, name, short_name, color, radii, radii_ionic):
            self.number = number
            self.name = name
            self.short_name = short_name
            self.color = color
            self.radii = radii
            self.radii_ionic = radii_ionic
    
    # This is the class, which stores the properties of one atom.
    class CLASS_atom_cluster_atom(object):  
        __slots__ = ('location')
        def __init__(self, location):
            self.location = location
    
    # -----------------------------------------------------------------------------
    #                                                                Read atom data
            
    def DEF_atom_read_atom_data():
    
    
        del ATOM_CLUSTER_ELEMENTS[:]
    
    
        for item in ATOM_CLUSTER_ELEMENTS_DEFAULT:
    
            # All three radii into a list
            radii = [item[4],item[5],item[6]]
            # The handling of the ionic radii will be done later. So far, it is an
            # empty list.
            radii_ionic = []
    
            li = CLASS_atom_cluster_Elements(item[0],item[1],item[2],item[3],
                                             radii,radii_ionic)
            ATOM_CLUSTER_ELEMENTS.append(li)
    
      
    # -----------------------------------------------------------------------------
    #                                                           Routines for shapes
    
    def vec_in_sphere(atom_pos,size, skin):
    
        regular = True
        inner   = True
    
    
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        if atom_pos.length > size/2.0:
    
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        if atom_pos.length < (size/2.0)*(1-skin):
    
            inner = False
    
        return (regular, inner)
    
    
    def vec_in_parabole(atom_pos, height, diameter):
    
        regular = True
        inner   = True
          
        px = atom_pos[0]  
        py = atom_pos[1]  
        pz = atom_pos[2] + height/2.0
        
        a = diameter / sqrt(4 * height)
        
        
        if pz < 0.0:
            return (False, False)
        if px == 0.0 and py == 0.0:
            return (True, True)
             
        if py == 0.0:
            y = 0.0
            x = a * a * pz / px
            z = x * x / (a * a)
        else:
            y = pz * py * a * a / (px*px + py*py)
            x = y * px / py
            z = (x*x + y*y) / (a * a)
        
        if( atom_pos.length > sqrt(x*x+y*y+z*z) ):
            regular = False
        
        return (regular, inner)
    
    
    def vec_in_pyramide_square(atom_pos, size, skin):
        
    
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        """
    
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        Please, if possible leave all this! The code documents the 
        mathemetical way of cutting a pyramide with square base.
    
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        P1 = Vector((-size/2, 0.0, -size/4))
        P2 = Vector((0.0, -size/2, -size/4))
        P4 = Vector((size/2, 0.0,  -size/4))
        P5 = Vector((0.0, size/2,  -size/4))
        P6 = Vector((0.0, 0.0,      size/4))
    
        # First face
        v11 = P1 - P2
        v12 = P1 - P6
        n1 = v11.cross(v12)
        g1 = -n1 * P1
        
        # Second face
        v21 = P6 - P4
        v22 = P6 - P5
        n2 = v21.cross(v22)
        g2 = -n2 * P6
    
        # Third face
        v31 = P1 - P5
        v32 = P1 - P6
        n3 = v32.cross(v31)
        g3 = -n3 * P1
        
        # Forth face
        v41 = P6 - P2
        v42 = P2 - P4
        n4 = v41.cross(v42)
        g4 = -n4 * P2
        
        # Fith face, base
        v51 = P2 - P1
        v52 = P2 - P4
        n5 = v51.cross(v52)
        g5 = -n5 * P2
    
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        """
     
    
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        # A much faster way for calculation:
    
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        size2 = size  * size
        size3 = size2 * size
    
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        n1 = Vector((-1/4, -1/4,  1/4)) * size2
    
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        g1 = -1/16 * size3
    
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        n2 = Vector(( 1/4,  1/4,  1/4)) * size2
    
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        g2 = g1
    
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        n3 = Vector((-1/4,  1/4,  1/4)) * size2
    
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        g3 = g1
    
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        n4 = Vector(( 1/4, -1/4,  1/4)) * size2
    
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        g4 = g1
    
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        n5 = Vector(( 0.0,  0.0, -1/2)) * size2
    
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        g5 = -1/8 * size3  
    
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        distance_plane_1 = abs((n1 * atom_pos - g1)/n1.length)
        on_plane_1 = (atom_pos - n1 * (distance_plane_1/n1.length)).length
        distance_plane_2 = abs((n2 * atom_pos - g2)/n2.length)
        on_plane_2 = (atom_pos - n2 * (distance_plane_2/n2.length)).length
        distance_plane_3 = abs((n3 * atom_pos - g3)/n3.length)
        on_plane_3 = (atom_pos - n3 * (distance_plane_3/n3.length)).length
        distance_plane_4 = abs((n4 * atom_pos - g4)/n4.length)
        on_plane_4 = (atom_pos - n4 * (distance_plane_4/n4.length)).length
        distance_plane_5 = abs((n5 * atom_pos - g5)/n5.length)
        on_plane_5 = (atom_pos - n5 * (distance_plane_5/n5.length)).length
    
    
        regular = True
        inner   = True
        if(atom_pos.length > on_plane_1):
            regular = False
        if(atom_pos.length > on_plane_2):
            regular = False
        if(atom_pos.length > on_plane_3):
            regular = False
        if(atom_pos.length > on_plane_4):
            regular = False
        if(atom_pos.length > on_plane_5):
            regular = False
    
        if skin == 1.0:
            return (regular, inner)
    
        size = size * (1.0 - skin)
        
    
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        size2 = size  * size
        size3 = size2 * size
    
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        n1 = Vector((-1/4, -1/4,  1/4)) * size2
    
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        g1 = -1/16 * size3
    
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        n2 = Vector(( 1/4,  1/4,  1/4)) * size2
    
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        g2 = g1
    
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        n3 = Vector((-1/4,  1/4,  1/4)) * size2
    
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        g3 = g1
    
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        n4 = Vector(( 1/4, -1/4,  1/4)) * size2
    
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        g4 = g1
    
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        n5 = Vector(( 0.0,  0.0, -1/2)) * size2
        g5 = -1/8 * size3  
    
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        distance_plane_1 = abs((n1 * atom_pos - g1)/n1.length)
        on_plane_1 = (atom_pos - n1 * (distance_plane_1/n1.length)).length
        distance_plane_2 = abs((n2 * atom_pos - g2)/n2.length)
        on_plane_2 = (atom_pos - n2 * (distance_plane_2/n2.length)).length
        distance_plane_3 = abs((n3 * atom_pos - g3)/n3.length)
        on_plane_3 = (atom_pos - n3 * (distance_plane_3/n3.length)).length
        distance_plane_4 = abs((n4 * atom_pos - g4)/n4.length)
        on_plane_4 = (atom_pos - n4 * (distance_plane_4/n4.length)).length
        distance_plane_5 = abs((n5 * atom_pos - g5)/n5.length)
        on_plane_5 = (atom_pos - n5 * (distance_plane_5/n5.length)).length
    
        
        inner = False
        if(atom_pos.length > on_plane_1):
            inner = True
        if(atom_pos.length > on_plane_2):
            inner = True
        if(atom_pos.length > on_plane_3):
            inner = True
        if(atom_pos.length > on_plane_4):
            inner = True
        if(atom_pos.length > on_plane_5):
            inner = True
    
        return (regular, inner)
    
    
    def vec_in_pyramide_hex_abc(atom_pos, size, skin):
        
        a = size/2.0
        #c = size/2.0*cos((30/360)*2.0*pi)
    
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        c = size * 0.4330127020
    
        #s = size/2.0*sin((30/360)*2.0*pi)  
        s = size * 0.25   
        #h = 2.0 * (sqrt(6.0)/3.0) * c
        h = 1.632993162 * c
    
    
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        """
        Please, if possible leave all this! The code documents the 
        mathemetical way of cutting a tetraeder.
    
    
        P1 = Vector((0.0,   a, 0.0))
        P2 = Vector(( -c,  -s, 0.0))
        P3 = Vector((  c,  -s, 0.0))    
        P4 = Vector((0.0, 0.0,  h))
        C = (P1+P2+P3+P4)/4.0
        P1 = P1 - C
        P2 = P2 - C
        P3 = P3 - C
        P4 = P4 - C
    
        # First face
        v11 = P1 - P2
        v12 = P1 - P4
        n1 = v11.cross(v12)
        g1 = -n1 * P1
        
        # Second face
        v21 = P2 - P3
        v22 = P2 - P4
        n2 = v21.cross(v22)
        g2 = -n2 * P2
    
        # Third face
        v31 = P3 - P1
        v32 = P3 - P4
        n3 = v31.cross(v32)
        g3 = -n3 * P3
        
        # Forth face
        v41 = P2 - P1
        v42 = P2 - P3
        n4 = v41.cross(v42)
        g4 = -n4 * P1
    
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        """
    
        n1 = Vector(( -h*(a+s),    c*h,    c*a     ))
        g1 = -1/2*c*(a*h+s*h)
        n2 = Vector((        0, -2*c*h,  2*c*s     ))
        g2 = -1/2*c*(a*h+s*h)
        n3 = Vector((  h*(a+s),    c*h,    a*c     ))
        g3 = -1/2*c*(a*h+s*h)
        n4 = Vector((        0,      0, -2*c*(s+a) ))
        g4 = -1/2*h*c*(s+a)
    
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        distance_plane_1 = abs((n1 * atom_pos - g1)/n1.length)
        on_plane_1 = (atom_pos - n1 * (distance_plane_1/n1.length)).length
        distance_plane_2 = abs((n2 * atom_pos - g2)/n2.length)
        on_plane_2 = (atom_pos - n2 * (distance_plane_2/n2.length)).length
        distance_plane_3 = abs((n3 * atom_pos - g3)/n3.length)
        on_plane_3 = (atom_pos - n3 * (distance_plane_3/n3.length)).length
        distance_plane_4 = abs((n4 * atom_pos - g4)/n4.length)
        on_plane_4 = (atom_pos - n4 * (distance_plane_4/n4.length)).length
    
    
        regular = True
        inner   = True
        if(atom_pos.length > on_plane_1):
            regular = False
        if(atom_pos.length > on_plane_2):
            regular = False
        if(atom_pos.length > on_plane_3):
            regular = False
        if(atom_pos.length > on_plane_4):
            regular = False
    
        if skin == 1.0:
            return (regular, inner)
    
        size = size * (1.0 - skin)
        
        a = size/2.0
        #c = size/2.0*cos((30/360)*2.0*pi)
        c= size * 0.4330127020
        #s = size/2.0*sin((30/360)*2.0*pi)  
        s = size * 0.25   
        #h = 2.0 * (sqrt(6.0)/3.0) * c
        h = 1.632993162 * c
    
    
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        n1 = Vector(( -h*(a+s),    c*h,    c*a     ))
        g1 = -1/2*c*(a*h+s*h)
        n2 = Vector((        0, -2*c*h,  2*c*s     ))
        g2 = -1/2*c*(a*h+s*h)
        n3 = Vector((  h*(a+s),    c*h,    a*c     ))
        g3 = -1/2*c*(a*h+s*h)
        n4 = Vector((        0,      0, -2*c*(s+a) ))
        g4 = -1/2*h*c*(s+a)
    
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        distance_plane_1 = abs((n1 * atom_pos - g1)/n1.length)
        on_plane_1 = (atom_pos - n1 * (distance_plane_1/n1.length)).length
        distance_plane_2 = abs((n2 * atom_pos - g2)/n2.length)
        on_plane_2 = (atom_pos - n2 * (distance_plane_2/n2.length)).length
        distance_plane_3 = abs((n3 * atom_pos - g3)/n3.length)
        on_plane_3 = (atom_pos - n3 * (distance_plane_3/n3.length)).length
        distance_plane_4 = abs((n4 * atom_pos - g4)/n4.length)
        on_plane_4 = (atom_pos - n4 * (distance_plane_4/n4.length)).length
    
        
        inner = False
        if(atom_pos.length > on_plane_1):
            inner = True
        if(atom_pos.length > on_plane_2):
            inner = True
        if(atom_pos.length > on_plane_3):
            inner = True
        if(atom_pos.length > on_plane_4):
            inner = True
    
        return (regular, inner)
        
    
    
    def vec_in_octahedron(atom_pos,size, skin):
    
        regular = True
        inner   = True
    
    
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        """
        Please, if possible leave all this! The code documents the 
        mathemetical way of cutting an octahedron.
    
    
        P1 = Vector((-size/2, 0.0, 0.0))
        P2 = Vector((0.0, -size/2, 0.0))
        P3 = Vector((0.0, 0.0, -size/2))
        P4 = Vector((size/2, 0.0, 0.0))
        P5 = Vector((0.0, size/2, 0.0))
        P6 = Vector((0.0, 0.0, size/2))
    
        # First face
        v11 = P2 - P1
        v12 = P2 - P3
        n1 = v11.cross(v12)
        g1 = -n1 * P2
        
        # Second face
        v21 = P1 - P5
        v22 = P1 - P3
        n2 = v21.cross(v22)
        g2 = -n2 * P1 
        
        # Third face
        v31 = P1 - P2
        v32 = P1 - P6
        n3 = v31.cross(v32)
        g3 = -n3 * P1
        
        # Forth face
        v41 = P6 - P2
        v42 = P2 - P4
        n4 = v41.cross(v42)
        g4 = -n4 * P2
    
        # Fith face
        v51 = P2 - P3
        v52 = P2 - P4
        n5 = v51.cross(v52)
        g5 = -n5 * P2
    
        # Six face
        v61 = P6 - P4
        v62 = P6 - P5
        n6 = v61.cross(v62)
        g6 = -n6 * P6
    
        # Seventh face
        v71 = P5 - P4
        v72 = P5 - P3
        n7 = v71.cross(v72)
        g7 = -n7 * P5
    
        # Eigth face
        v81 = P1 - P5
        v82 = P1 - P6
        n8 = v82.cross(v81)
        g8 = -n8 * P1
    
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        """
     
        # A much faster way for calculation:
        size2 = size  * size
        size3 = size2 * size
        n1 = Vector((-1/4, -1/4, -1/4)) * size2
        g1 = -1/8 * size3
        n2 = Vector((-1/4,  1/4, -1/4)) * size2
        g2 = g1
        n3 = Vector((-1/4, -1/4,  1/4)) * size2
        g3 = g1
        n4 = Vector(( 1/4, -1/4,  1/4)) * size2
        g4 = g1
        n5 = Vector(( 1/4, -1/4, -1/4)) * size2
        g5 = g1
        n6 = Vector(( 1/4,  1/4,  1/4)) * size2
        g6 = g1
        n7 = Vector(( 1/4,  1/4, -1/4)) * size2
        g7 = g1
        n8 = Vector((-1/4,  1/4,  1/4)) * size2
        g8 = g1
    
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        distance_plane_1 = abs((n1 * atom_pos - g1)/n1.length)
        on_plane_1 = (atom_pos - n1 * (distance_plane_1/n1.length)).length
        distance_plane_2 = abs((n2 * atom_pos - g2)/n2.length)
        on_plane_2 = (atom_pos - n2 * (distance_plane_2/n2.length)).length
        distance_plane_3 = abs((n3 * atom_pos - g3)/n3.length)
        on_plane_3 = (atom_pos - n3 * (distance_plane_3/n3.length)).length
        distance_plane_4 = abs((n4 * atom_pos - g4)/n4.length)
        on_plane_4 = (atom_pos - n4 * (distance_plane_4/n4.length)).length
        distance_plane_5 = abs((n5 * atom_pos - g5)/n5.length)
        on_plane_5 = (atom_pos - n5 * (distance_plane_5/n5.length)).length
        distance_plane_6 = abs((n6 * atom_pos - g6)/n6.length)
        on_plane_6 = (atom_pos - n6 * (distance_plane_6/n6.length)).length
        distance_plane_7 = abs((n7 * atom_pos - g7)/n7.length)
        on_plane_7 = (atom_pos - n7 * (distance_plane_7/n7.length)).length
        distance_plane_8 = abs((n8 * atom_pos - g8)/n8.length)
        on_plane_8 = (atom_pos - n8 * (distance_plane_8/n8.length)).length
    
    
        if(atom_pos.length > on_plane_1):
            regular = False
        if(atom_pos.length > on_plane_2):
            regular = False
        if(atom_pos.length > on_plane_3):
            regular = False
        if(atom_pos.length > on_plane_4):
            regular = False
        if(atom_pos.length > on_plane_5):
            regular = False
        if(atom_pos.length > on_plane_6):
            regular = False
        if(atom_pos.length > on_plane_7):
            regular = False
        if(atom_pos.length > on_plane_8):
            regular = False
    
        if skin == 1.0:
            return (regular, inner)
    
        size = size * (1.0 - skin)
    
    
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        size2 = size  * size
        size3 = size2 * size
        n1 = Vector((-1/4, -1/4, -1/4)) * size2
        g1 = -1/8 * size3
        n2 = Vector((-1/4,  1/4, -1/4)) * size2
        g2 = g1
        n3 = Vector((-1/4, -1/4,  1/4)) * size2
        g3 = g1
        n4 = Vector(( 1/4, -1/4,  1/4)) * size2
        g4 = g1
        n5 = Vector(( 1/4, -1/4, -1/4)) * size2
        g5 = g1
        n6 = Vector(( 1/4,  1/4,  1/4)) * size2
        g6 = g1
        n7 = Vector(( 1/4,  1/4, -1/4)) * size2
        g7 = g1
        n8 = Vector((-1/4,  1/4,  1/4)) * size2
        g8 = g1
    
        distance_plane_1 = abs((n1 * atom_pos - g1)/n1.length)
        on_plane_1 = (atom_pos - n1 * (distance_plane_1/n1.length)).length
        distance_plane_2 = abs((n2 * atom_pos - g2)/n2.length)
        on_plane_2 = (atom_pos - n2 * (distance_plane_2/n2.length)).length
        distance_plane_3 = abs((n3 * atom_pos - g3)/n3.length)
        on_plane_3 = (atom_pos - n3 * (distance_plane_3/n3.length)).length
        distance_plane_4 = abs((n4 * atom_pos - g4)/n4.length)
        on_plane_4 = (atom_pos - n4 * (distance_plane_4/n4.length)).length
        distance_plane_5 = abs((n5 * atom_pos - g5)/n5.length)
        on_plane_5 = (atom_pos - n5 * (distance_plane_5/n5.length)).length
        distance_plane_6 = abs((n6 * atom_pos - g6)/n6.length)
        on_plane_6 = (atom_pos - n6 * (distance_plane_6/n6.length)).length
        distance_plane_7 = abs((n7 * atom_pos - g7)/n7.length)
        on_plane_7 = (atom_pos - n7 * (distance_plane_7/n7.length)).length
        distance_plane_8 = abs((n8 * atom_pos - g8)/n8.length)
        on_plane_8 = (atom_pos - n8 * (distance_plane_8/n8.length)).length
    
    
        inner = False
        if(atom_pos.length > on_plane_1):
            inner = True
        if(atom_pos.length > on_plane_2):
            inner = True
        if(atom_pos.length > on_plane_3):
            inner = True
        if(atom_pos.length > on_plane_4):
            inner = True
        if(atom_pos.length > on_plane_5):
            inner = True
        if(atom_pos.length > on_plane_6):
            inner = True
        if(atom_pos.length > on_plane_7):
            inner = True
        if(atom_pos.length > on_plane_8):
            inner = True
    
        return (regular, inner)
    
    
    def vec_in_truncated_octahedron(atom_pos,size, skin):
    
        regular = True
        inner   = True
    
        # The normal octahedron
    
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        size2 = size  * size
        size3 = size2 * size
        n1 = Vector((-1/4, -1/4, -1/4)) * size2
        g1 = -1/8 * size3
        n2 = Vector((-1/4,  1/4, -1/4)) * size2
        g2 = g1
        n3 = Vector((-1/4, -1/4,  1/4)) * size2
        g3 = g1
        n4 = Vector(( 1/4, -1/4,  1/4)) * size2
        g4 = g1
        n5 = Vector(( 1/4, -1/4, -1/4)) * size2
        g5 = g1
        n6 = Vector(( 1/4,  1/4,  1/4)) * size2
        g6 = g1
        n7 = Vector(( 1/4,  1/4, -1/4)) * size2
        g7 = g1
        n8 = Vector((-1/4,  1/4,  1/4)) * size2
        g8 = g1
    
        distance_plane_1 = abs((n1 * atom_pos - g1)/n1.length)
        on_plane_1 = (atom_pos - n1 * (distance_plane_1/n1.length)).length
        distance_plane_2 = abs((n2 * atom_pos - g2)/n2.length)
        on_plane_2 = (atom_pos - n2 * (distance_plane_2/n2.length)).length
        distance_plane_3 = abs((n3 * atom_pos - g3)/n3.length)
        on_plane_3 = (atom_pos - n3 * (distance_plane_3/n3.length)).length
        distance_plane_4 = abs((n4 * atom_pos - g4)/n4.length)
        on_plane_4 = (atom_pos - n4 * (distance_plane_4/n4.length)).length
        distance_plane_5 = abs((n5 * atom_pos - g5)/n5.length)
        on_plane_5 = (atom_pos - n5 * (distance_plane_5/n5.length)).length
        distance_plane_6 = abs((n6 * atom_pos - g6)/n6.length)
        on_plane_6 = (atom_pos - n6 * (distance_plane_6/n6.length)).length
        distance_plane_7 = abs((n7 * atom_pos - g7)/n7.length)
        on_plane_7 = (atom_pos - n7 * (distance_plane_7/n7.length)).length
        distance_plane_8 = abs((n8 * atom_pos - g8)/n8.length)
        on_plane_8 = (atom_pos - n8 * (distance_plane_8/n8.length)).length
    
    
        # Here are the 6 additional faces
    
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        # pp = (size/2.0) - (sqrt(2.0)/2.0) * ((size/sqrt(2.0))/3.0)
        pp = size / 3.0
    
    
        n_1 = Vector((1.0,0.0,0.0)) 
        n_2 = Vector((-1.0,0.0,0.0))           
        n_3 = Vector((0.0,1.0,0.0))    
        n_4 = Vector((0.0,-1.0,0.0))
        n_5 = Vector((0.0,0.0,1.0))    
        n_6 = Vector((0.0,0.0,-1.0))   
    
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        distance_plane_1b = abs((n_1 * atom_pos + pp)/n_1.length)
        on_plane_1b = (atom_pos - n_1 * (distance_plane_1b/n_1.length)).length
        distance_plane_2b = abs((n_2 * atom_pos + pp)/n_2.length)
        on_plane_2b = (atom_pos - n_2 * (distance_plane_2b/n_2.length)).length
        distance_plane_3b = abs((n_3 * atom_pos + pp)/n_3.length)
        on_plane_3b = (atom_pos - n_3 * (distance_plane_3b/n_3.length)).length
        distance_plane_4b = abs((n_4 * atom_pos + pp)/n_4.length)
        on_plane_4b = (atom_pos - n_4 * (distance_plane_4b/n_4.length)).length
        distance_plane_5b = abs((n_5 * atom_pos + pp)/n_5.length)
        on_plane_5b = (atom_pos - n_5 * (distance_plane_5b/n_5.length)).length
        distance_plane_6b = abs((n_6 * atom_pos + pp)/n_6.length)
        on_plane_6b = (atom_pos - n_6 * (distance_plane_6b/n_6.length)).length
    
    
        if(atom_pos.length > on_plane_1):
            regular = False
        if(atom_pos.length > on_plane_2):
            regular = False
        if(atom_pos.length > on_plane_3):
            regular = False
        if(atom_pos.length > on_plane_4):
            regular = False
        if(atom_pos.length > on_plane_5):
            regular = False
        if(atom_pos.length > on_plane_6):
            regular = False
        if(atom_pos.length > on_plane_7):
            regular = False
        if(atom_pos.length > on_plane_8):
            regular = False
        if(atom_pos.length > on_plane_1b):
            regular = False
        if(atom_pos.length > on_plane_2b):
            regular = False
        if(atom_pos.length > on_plane_3b):
            regular = False
        if(atom_pos.length > on_plane_4b):
            regular = False
        if(atom_pos.length > on_plane_5b):
            regular = False
        if(atom_pos.length > on_plane_6b):
            regular = False
    
        if skin == 1.0:
            return (regular, inner)
    
        size = size * (1.0 - skin)
        
    
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        # The normal octahedron
        size2 = size  * size
        size3 = size2 * size
        n1 = Vector((-1/4, -1/4, -1/4)) * size2
        g1 = -1/8 * size3
        n2 = Vector((-1/4,  1/4, -1/4)) * size2
        g2 = g1
        n3 = Vector((-1/4, -1/4,  1/4)) * size2
        g3 = g1
        n4 = Vector(( 1/4, -1/4,  1/4)) * size2
        g4 = g1
        n5 = Vector(( 1/4, -1/4, -1/4)) * size2
        g5 = g1
        n6 = Vector(( 1/4,  1/4,  1/4)) * size2
        g6 = g1
        n7 = Vector(( 1/4,  1/4, -1/4)) * size2
        g7 = g1
        n8 = Vector((-1/4,  1/4,  1/4)) * size2
        g8 = g1
    
        distance_plane_1 = abs((n1 * atom_pos - g1)/n1.length)
        on_plane_1 = (atom_pos - n1 * (distance_plane_1/n1.length)).length
        distance_plane_2 = abs((n2 * atom_pos - g2)/n2.length)
        on_plane_2 = (atom_pos - n2 * (distance_plane_2/n2.length)).length
        distance_plane_3 = abs((n3 * atom_pos - g3)/n3.length)
        on_plane_3 = (atom_pos - n3 * (distance_plane_3/n3.length)).length
        distance_plane_4 = abs((n4 * atom_pos - g4)/n4.length)
        on_plane_4 = (atom_pos - n4 * (distance_plane_4/n4.length)).length
        distance_plane_5 = abs((n5 * atom_pos - g5)/n5.length)
        on_plane_5 = (atom_pos - n5 * (distance_plane_5/n5.length)).length
        distance_plane_6 = abs((n6 * atom_pos - g6)/n6.length)
        on_plane_6 = (atom_pos - n6 * (distance_plane_6/n6.length)).length
        distance_plane_7 = abs((n7 * atom_pos - g7)/n7.length)
        on_plane_7 = (atom_pos - n7 * (distance_plane_7/n7.length)).length
        distance_plane_8 = abs((n8 * atom_pos - g8)/n8.length)
        on_plane_8 = (atom_pos - n8 * (distance_plane_8/n8.length)).length
    
    
        # Here are the 6 additional faces
        # pp = (size/2.0) - (sqrt(2.0)/2.0) * ((size/sqrt(2.0))/3.0)
        pp = size / 3.0
    
        n_1 = Vector((1.0,0.0,0.0)) 
        n_2 = Vector((-1.0,0.0,0.0))           
        n_3 = Vector((0.0,1.0,0.0))    
        n_4 = Vector((0.0,-1.0,0.0))
        n_5 = Vector((0.0,0.0,1.0))    
        n_6 = Vector((0.0,0.0,-1.0))   
        
    
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        distance_plane_1b = abs((n_1 * atom_pos + pp)/n_1.length)
        on_plane_1b = (atom_pos - n_1 * (distance_plane_1b/n_1.length)).length
        distance_plane_2b = abs((n_2 * atom_pos + pp)/n_2.length)
        on_plane_2b = (atom_pos - n_2 * (distance_plane_2b/n_2.length)).length
        distance_plane_3b = abs((n_3 * atom_pos + pp)/n_3.length)
        on_plane_3b = (atom_pos - n_3 * (distance_plane_3b/n_3.length)).length
        distance_plane_4b = abs((n_4 * atom_pos + pp)/n_4.length)
        on_plane_4b = (atom_pos - n_4 * (distance_plane_4b/n_4.length)).length
        distance_plane_5b = abs((n_5 * atom_pos + pp)/n_5.length)
        on_plane_5b = (atom_pos - n_5 * (distance_plane_5b/n_5.length)).length
        distance_plane_6b = abs((n_6 * atom_pos + pp)/n_6.length)
        on_plane_6b = (atom_pos - n_6 * (distance_plane_6b/n_6.length)).length
    
    
        inner = False
    
        if(atom_pos.length > on_plane_1):
            inner = True
        if(atom_pos.length > on_plane_2):
            inner = True
        if(atom_pos.length > on_plane_3):
            inner = True
        if(atom_pos.length > on_plane_4):
            inner = True
        if(atom_pos.length > on_plane_5):
            inner = True
        if(atom_pos.length > on_plane_6):
            inner = True
        if(atom_pos.length > on_plane_7):
            inner = True
        if(atom_pos.length > on_plane_8):
            inner = True
        if(atom_pos.length > on_plane_1b):
            inner = True
        if(atom_pos.length > on_plane_2b):
            inner = True
        if(atom_pos.length > on_plane_3b):
            inner = True
        if(atom_pos.length > on_plane_4b):
            inner = True
        if(atom_pos.length > on_plane_5b):
            inner = True
        if(atom_pos.length > on_plane_6b):
            inner = True
        
        return (regular, inner)
    
    # -----------------------------------------------------------------------------
    #                                                         Routines for lattices
    
    def create_hexagonal_abcabc_lattice(ctype, size, skin, lattice):
    
        atom_number_total = 0
        atom_number_drawn = 0
        y_displ = 0
        z_displ = 0
    
        """
        e = (1/sqrt(2.0)) * lattice
        f = sqrt(3.0/4.0) * e
        df1 = (e/2.0) * tan((30.0/360.0)*2.0*pi)
        df2 = (e/2.0) / cos((30.0/360.0)*2.0*pi)
        g = sqrt(2.0/3.0) * e
        """
    
        e = 0.7071067810 * lattice
        f = 0.8660254038 * e
        df1 = 0.2886751348 * e
        df2 = 0.5773502690 * e
        g = 0.8164965810 * e
    
        if ctype == "parabolid_abc":
            # size = height, skin = diameter
            number_x = int(skin/(2*e))+4
            number_y = int(skin/(2*f))+4
            number_z = int(size/(2*g))
        else:
            number_x = int(size/(2*e))+4
            number_y = int(size/(2*f))+4
            number_z = int(size/(2*g))+1+4
    
    
        for k in range(-number_z,number_z+1):
            for j in range(-number_y,number_y+1):
                for i in range(-number_x,number_x+1):
                    atom = Vector((float(i)*e,float(j)*f,float(k)*g)) 
    
                    if y_displ == 1:
                        if z_displ == 1:
                            atom[0] += e/2.0  
                        else:
                            atom[0] -= e/2.0
                    if z_displ == 1:
                        atom[0] -= e/2.0
                        atom[1] += df1
                    if z_displ == 2:
                        atom[0] += 0.0
                        atom[1] += df2
    
                    if ctype == "sphere_hex_abc":
                        message = vec_in_sphere(atom, size, skin)
                    elif ctype == "pyramide_hex_abc":
                        # size = height, skin = diameter
                        message = vec_in_pyramide_hex_abc(atom, size, skin)
                    elif ctype == "parabolid_abc":
                        message = vec_in_parabole(atom, size, skin)          
    
                    if message[0] == True and message[1] == True:
                        atom_add = CLASS_atom_cluster_atom(atom)
                        ATOM_CLUSTER_ALL_ATOMS.append(atom_add)
                        atom_number_total += 1
                        atom_number_drawn += 1
                    if message[0] == True and message[1] == False:
                        atom_number_total += 1                 
              
                if y_displ == 1:
                    y_displ = 0
                else:
                    y_displ = 1
    
            y_displ = 0
            if z_displ == 0:
               z_displ = 1
            elif z_displ == 1:
               z_displ = 2
            else:
               z_displ = 0
    
    
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        print("Atom positions calculated")
    
    
        return (atom_number_total, atom_number_drawn)
    
    
    def create_hexagonal_abab_lattice(ctype, size, skin, lattice):
    
        atom_number_total = 0
        atom_number_drawn = 0
        y_displ = "even"
        z_displ = "even"
    
        """
        e = (1/sqrt(2.0)) * lattice
        f = sqrt(3.0/4.0) * e
        df = (e/2.0) * tan((30.0/360.0)*2*pi)
        g = sqrt(2.0/3.0) * e
        """
    
        e = 0.7071067814 * lattice
        f = 0.8660254038 * e
        df = 0.2886751348 * e
        g = 0.8164965810 * e
    
    
        if ctype == "parabolid_ab":
            # size = height, skin = diameter
            number_x = int(skin/(2*e))+4
            number_y = int(skin/(2*f))+4
            number_z = int(size/(2*g))
        else:
            number_x = int(size/(2*e))+4
            number_y = int(size/(2*f))+4
            number_z = int(size/(2*g))+1+4
    
    
        for k in range(-number_z,number_z+1):
            for j in range(-number_y,number_y+1):
                for i in range(-number_x,number_x+1):
    
                    atom = Vector((float(i)*e,float(j)*f,float(k)*g))
              
                    if "odd" in y_displ:
                        if "odd" in z_displ:
                            atom[0] += e/2.0  
                        else:
                            atom[0] -= e/2.0
                    if "odd" in z_displ:
                        atom[0] -= e/2.0