spaceGroupD3.py

spacegroups={'1':['x,y,z'],
            '2':['x,y,z',
                '-x,-y,-z'],
            '3':['x,y,z',
                '-x,y,-z'],
            '4':['x,y,z',
                '-x,y+0.5,-z'],
            '5':['x,y,z',
                '-x,y,-z',
                'x+0.5,y+0.5,z',
                '-x+0.5,y+0.5,-z'],
            '6':['x,y,z',
                'x,-y,z'],
            '7':['x,y,z',
                'x,-y,z+0.5'],
            '8':['x,y,z',
                'x,-y,z',
                'x+0.5,y+0.5,z',
                'x+0.5,-y+0.5,z'],
            '9':['x,y,z',
                'x,-y,z',
                'x+0.5,y+0.5,z',
                'x+0.5,-y+0.5,z'],
            '10':['x,y,z',
                '-x,y,-z',
                '-x,-y,-z',
                'x,-y,z'],
            '11':['x,y,z',
                '-x,y+0.5,-z',
                '-x,-y,-z',
                'x,-y+0.5,z'],
            '12':['x,y,z',
                '-x,y,-z',
                '-x,-y,-z',
                'x,-y,z',
                'x+0.5,y+0.5,z',
                '-x+0.5,y+0.5,-z',
                '-x+0.5,-y+0.5,-z',
                'x+0.5,-y+0.5,z'],
            '13':['x,y,z',
                '-x,y,-z+0.5',
                '-x,-y,-z',
                'x,-y,z+0.5'],
            '14':['x,y,z',
                '-x,y+0.5,-z+0.5',
                '-x,-y,-z',
                'x,-y+0.5,z+0.5'],
            '15':['x,y,z',
                '-x,y,-z+0.5',
                '-x,-y,-z',
                'x,-y,z+0.5',
                'x+0.5,y+0.5,z',
                '-x+0.5,y+0.5,-z+0.5',
                '-x+0.5,-y+0.5,-z',
                'x+0.5,-y+0.5,z+0.5'],
            '16':['x,y,z',
                '-x,-y,z',
                '-x,y,-z',
                'x,-y,-z'],
            '17':['x,y,z',
                '-x,-y,z+0.5',
                '-x,y,-z+0.5',
                'x,-y,-z'],
            '18':['x,y,z',
                '-x,-y,z',
                '-x+0.5,y+0.5,-z',
                'x+0.5,-y+0.5,-z'],
            '19':['x,y,z',
                '-x+0.5,-y,z+0.5',
                '-x,y+0.5,-z+0.5',
                'x+0.5,-y+0.5,-z'],
            '20':['x,y,z',
                '-x,-y,z+0.5',
                '-x,y,-z+0.5',
                'x,-y,-z',
                'x+0.5,y+0.5,z',
                '-x+0.5,-y+0.5,z+0.5',
                '-x+0.5,y+0.5,-z+0.5',
                'x+0.5,-y+0.5,-z'],
            '21':['x,y,z',
                '-x,-y,z',
                '-x,y,-z',
                'x,-y,-z',
                'x+0.5,y+0.5,z',
                '-x+0.5,-y+0.5,z',
                '-x+0.5,y+0.5,-z',
                'x+0.5,-y+0.5,-z'],
            '22':['x,y,z',
                '-x,-y,z',
                '-x,y,-z',
                'x,-y,-z',
                'x,y+0.5,z+0.5',
                '-x,-y+0.5,z+0.5',
                '-x,y+0.5,-z+0.5',
                'x,-y+0.5,-z+0.5',
                'x+0.5,y,z+0.5',
                '-x+0.5,-y,z+0.5',
                '-x+0.5,y,-z+0.5',
                'x+0.5,-y,-z+0.5',
                'x+0.5,y+0.5,z',
                '-x+0.5,-y+0.5,z',
                '-x+0.5,y+0.5,-z',
                'x+0.5,-y+0.5,-z'],
            '23':['x,y,z',
                '-x,-y,z',
                '-x,y,-z',
                'x,-y,-z',
                'x+0.5,y+0.5,z+0.5',
                '-x+0.5,-y+0.5,z+0.5',
                '-x+0.5,y+0.5,-z+0.5',
                'x+0.5,-y+0.5,-z+0.5'],
            '24':['x,y,z',
                '-x+0.5,-y,z+0.5',
                '-x,y+0.5,-z+0.5',
                'x+0.5,-y+0.5,-z',
                'x+0.5,y+0.5,z+0.5',
                '-x,-y+0.5,z',
                '-x+0.5,y,-z',
                'x,-y,-z+0.5'],
            '25':['x,y,z',
                '-x,-y,z',
                'x,-y,z',
                '-x,y,z'],
            '26':['x,y,z',
                '-x,-y,z+0.5',
                'x,-y,z+0.5',
                '-x,y,z'],
            '27':['x,y,z',
                '-x,-y,z',
                'x,-y,z+0.5',
                '-x,y,z+0.5'],
            '28':['x,y,z',
                '-x,-y,z',
                'x+0.5,-y,z',
                '-x+0.5,y,z'],
            '29':['x,y,z',
                '-x,-y,z+0.5',
                'x+0.5,-y,z',
                '-x+0.5,y,z+0.5'],
            '30':['x,y,z',
                '-x,-y,z',
                'x,-y+0.5,z+0.5',
                '-x,y+0.5,z+0.5'],
            '31':['x,y,z',
                '-x+0.5,-y,z+0.5',
                'x+0.5,-y,z+0.5',
                '-x,y,z'],
            '32':['x,y,z',
                '-x,-y,z',
                'x+0.5,-y+0.5,z',
                '-x+0.5,y+0.5,z'],
            '33':['x,y,z',
                '-x,-y,z+0.5',
                'x+0.5,-y+0.5,z',
                '-x+0.5,y+0.5,z+0.5'],
            '34':['x,y,z',
                '-x,-y,z',
                'x+0.5,-y+0.5,z+0.5',
                '-x+0.5,y+0.5,z+0.5'],
            '35':['x,y,z',
                '-x,-y,z',
                'x,-y,z',
                '-x,y,z',
                'x+0.5,y+0.5,z',
                '-x+0.5,-y+0.5,z',
                'x+0.5,-y+0.5,z',
                '-x+0.5,y+0.5,z'],
            '36':['x,y,z',
                '-x,-y,z+0.5',
                'x,-y,z+0.5',
                '-x,y,z',
                'x+0.5,y+0.5,z',
                '-x+0.5,-y+0.5,z+0.5',
                'x+0.5,-y+0.5,z+0.5',
                '-x+0.5,y+0.5,z'],
            '37':['x,y,z',
                '-x,-y,z',
                'x,-y,z+0.5',
                '-x,y,z+0.5',
                'x+0.5,y+0.5,z',
                '-x+0.5,-y+0.5,z',
                'x+0.5,-y+0.5,z+0.5',
                '-x+0.5,y+0.5,z+0.5'],
            '38':['x,y,z',
                '-x,-y,z',
                'x,-y,z',
                '-x,y,z',
                'x,y+0.5,z+0.5',
                '-x,-y+0.5,z+0.5',
                'x,-y+0.5,z+0.5',
                '-x,y+0.5,z+0.5'],
            '39':['x,y,z',
                '-x,-y,z',
                'x,-y+0.5,z',
                '-x,y+0.5,z',
                'x,y+0.5,z+0.5',
                '-x,-y+0.5,z+0.5',
                'x,-y,z+0.5',
                '-x,y,z+0.5'],
            '40':['x,y,z',
                '-x,-y,z',
                'x+0.5,-y,z',
                '-x+0.5,y,z',
                'x,y+0.5,z+0.5',
                '-x,-y+0.5,z+0.5',
                'x+0.5,-y+0.5,z+0.5',
                '-x+0.5,y+0.5,z+0.5'],
            '41':['x,y,z',
                '-x,-y,z',
                'x+0.5,-y+0.5,z',
                '-x+0.5,y+0.5,z',
                'x,y+0.5,z+0.5',
                '-x,-y+0.5,z+0.5',
                'x+0.5,-y,z+0.5',
                '-x+0.5,y,z+0.5'],
            '42':['x,y,z',
                '-x,-y,z',
                'x,-y,z',
                '-x,y,z',
                'x,y+0.5,z+0.5',
                '-x,-y+0.5,z+0.5',
                'x,-y+0.5,z+0.5',
                '-x,y+0.5,z+0.5',
                'x+0.5,y,z+0.5',
                '-x+0.5,-y,z+0.5',
                'x+0.5,-y,z+0.5',
                '-x+0.5,y,z+0.5',
                'x+0.5,y+0.5,z',
                '-x+0.5,-y+0.5,z',
                'x+0.5,-y+0.5,z',
                '-x+0.5,y+0.5,z'],
            '43':['x,y,z',
                '-x,-y,z',
                'x+0.25,-y+0.25,z+0.25',
                '-x+0.25,y+0.25,z+0.25',
                'x,y+0.5,z+0.5',
                '-x,-y+0.5,z+0.5',
                'x+0.25,-y+0.75,z+0.75',
                '-x+0.25,y+0.75,z+0.75',
                'x+0.5,y,z+0.5',
                '-x+0.5,-y,z+0.5',
                'x+0.75,-y+0.25,z+0.75',
                '-x+0.75,y+0.25,z+0.75',
                'x+0.5,y+0.5,z',
                '-x+0.5,-y+0.5,z',
                'x+0.75,-y+0.75,z+0.25',
                '-x+0.75,y+0.75,z+0.25'],
            '44':['x,y,z',
                '-x,-y,z',
                'x,-y,z',
                '-x,y,z',
                'x+0.5,y+0.5,z+0.5',
                '-x+0.5,-y+0.5,z+0.5',
                'x+0.5,-y+0.5,z+0.5',
                '-x+0.5,y+0.5,z+0.5'],
            '45':['x,y,z',
                '-x,-y,z',
                'x+0.5,-y+0.5,z',
                '-x+0.5,y+0.5,z',
                'x+0.5,y+0.5,z+0.5',
                '-x+0.5,-y+0.5,z+0.5',
                'x,-y,z+0.5',
                '-x,y,z+0.5'],
            '46':['x,y,z',
                '-x,-y,z',
                'x+0.5,-y,z',
                '-x+0.5,y,z',
                'x+0.5,y+0.5,z+0.5',
                '-x+0.5,-y+0.5,z+0.5',
                'x,-y+0.5,z+0.5',
                '-x,y+0.5,z+0.5'],
            '47':['x,y,z',
                '-x,-y,z',
                '-x,y,-z',
                'x,-y,-z',
                '-x,-y,-z',
                'x,y,-z',
                'x,-y,z',
                '-x,y,z'],
            '48':['x,y,z',
                '-x+0.5,-y+0.5,z',
                '-x+0.5,y,-z+0.5',
                'x,-y+0.5,-z+0.5',
                '-x,-y,-z',
                'x+0.5,y+0.5,-z',
                'x+0.5,-y,z+0.5',
                '-x,y+0.5,z+0.5'],
            '49':['x,y,z',
                '-x,-y,z',
                '-x,y,-z+0.5',
                'x,-y,-z+0.5',
                '-x,-y,-z',
                'x,y,-z',
                'x,-y,z+0.5',
                '-x,y,z+0.5'],
            '50':['x,y,z',
                '-x+0.5,-y+0.5,z',
                '-x+0.5,y,-z',
                'x,-y+0.5,-z',
                '-x,-y,-z',
                'x+0.5,y+0.5,-z',
                'x+0.5,-y,z',
                '-x,y+0.5,z'],
            '51':['x,y,z',
                '-x+0.5,-y,z',
                '-x,y,-z',
                'x+0.5,-y,-z',
                '-x,-y,-z',
                'x+0.5,y,-z',
                'x,-y,z',
                '-x+0.5,y,z'],
            '52':['x,y,z',
                '-x+0.5,-y,z',
                '-x+0.5,y+0.5,-z+0.5',
                'x,-y+0.5,-z+0.5',
                '-x,-y,-z',
                'x+0.5,y,-z',
                'x+0.5,-y+0.5,z+0.5',
                '-x,y+0.5,z+0.5'],
            '53':['x,y,z',
                '-x+0.5,-y,z+0.5',
                '-x+0.5,y,-z+0.5',
                'x,-y,-z',
                '-x,-y,-z',
                'x+0.5,y,-z+0.5',
                'x+0.5,-y,z+0.5',
                '-x,y,z'],
            '54':['x,y,z',
                '-x+0.5,-y,z',
                '-x,y,-z+0.5',
                'x+0.5,-y,-z+0.5',
                '-x,-y,-z',
                'x+0.5,y,-z',
                'x,-y,z+0.5',
                '-x+0.5,y,z+0.5'],
            '55':['x,y,z',
                '-x,-y,z',
                '-x+0.5,y+0.5,-z',
                'x+0.5,-y+0.5,-z',
                '-x,-y,-z',
                'x,y,-z',
                'x+0.5,-y+0.5,z',
                '-x+0.5,y+0.5,z'],
            '56':['x,y,z',
                '-x+0.5,-y+0.5,z',
                '-x,y+0.5,-z+0.5',
                'x+0.5,-y,-z+0.5',
                '-x,-y,-z',
                'x+0.5,y+0.5,-z',
                'x,-y+0.5,z+0.5',
                '-x+0.5,y,z+0.5'],
            '57':['x,y,z',
                '-x,-y,z+0.5',
                '-x,y+0.5,-z+0.5',
                'x,-y+0.5,-z',
                '-x,-y,-z',
                'x,y,-z+0.5',
                'x,-y+0.5,z+0.5',
                '-x,y+0.5,z'],
            '58':['x,y,z',
                '-x,-y,z',
                '-x+0.5,y+0.5,-z+0.5',
                'x+0.5,-y+0.5,-z+0.5',
                '-x,-y,-z',
                'x,y,-z',
                'x+0.5,-y+0.5,z+0.5',
                '-x+0.5,y+0.5,z+0.5'],
            '59':['x,y,z',
                '-x+0.5,-y+0.5,z',
                '-x,y+0.5,-z',
                'x+0.5,-y,-z',
                '-x,-y,-z',
                'x+0.5,y+0.5,-z',
                'x,-y+0.5,z',
                '-x+0.5,y,z'],
            '60':['x,y,z',
                '-x+0.5,-y+0.5,z+0.5',
                '-x,y,-z+0.5',
                'x+0.5,-y+0.5,-z',
                '-x,-y,-z',
                'x+0.5,y+0.5,-z+0.5',
                'x,-y,z+0.5',
                '-x+0.5,y+0.5,z'],
            '61':['x,y,z',
                '-x+0.5,-y,z+0.5',
                '-x,y+0.5,-z+0.5',
                'x+0.5,-y+0.5,-z',
                '-x,-y,-z',
                'x+0.5,y,-z+0.5',
                'x,-y+0.5,z+0.5',
                '-x+0.5,y+0.5,z'],
            '62':['x,y,z',
                '-x+0.5,-y,z+0.5',
                '-x,y+0.5,-z',
                'x+0.5,-y+0.5,-z+0.5',
                '-x,-y,-z',
                'x+0.5,y,-z+0.5',
                'x,-y+0.5,z',
                '-x+0.5,y+0.5,z+0.5'],
            '63':['x,y,z',
                '-x,-y,z+0.5',
                '-x,y,-z+0.5',
                'x,-y,-z',
                '-x,-y,-z',
                'x,y,-z+0.5',
                'x,-y,z+0.5',
                '-x,y,z',
                'x+0.5,y+0.5,z',
                '-x+0.5,-y+0.5,z+0.5',
                '-x+0.5,y+0.5,-z+0.5',
                'x+0.5,-y+0.5,-z',
                '-x+0.5,-y+0.5,-z',
                'x+0.5,y+0.5,-z+0.5',
                'x+0.5,-y+0.5,z+0.5',
                '-x+0.5,y+0.5,z'],
            '64':['x,y,z',
                '-x,-y+0.5,z+0.5',
                '-x,y+0.5,-z+0.5',
                'x,-y,-z',
                '-x,-y,-z',
                'x,y+0.5,-z+0.5',
                'x,-y+0.5,z+0.5',
                '-x,y,z',
                'x+0.5,y+0.5,z',
                '-x+0.5,-y,z+0.5',
                '-x+0.5,y,-z+0.5',
                'x+0.5,-y+0.5,-z',
                '-x+0.5,-y+0.5,-z',
                'x+0.5,y,-z+0.5',
                'x+0.5,-y,z+0.5',
                '-x+0.5,y+0.5,z'],
            '65':['x,y,z',
                '-x,-y,z',
                '-x,y,-z',
                'x,-y,-z',
                '-x,-y,-z',
                'x,y,-z',
                'x,-y,z',
                '-x,y,z',
                'x+0.5,y+0.5,z',
                '-x+0.5,-y+0.5,z',
                '-x+0.5,y+0.5,-z',
                'x+0.5,-y+0.5,-z',
                '-x+0.5,-y+0.5,-z',
                'x+0.5,y+0.5,-z',
                'x+0.5,-y+0.5,z',
                '-x+0.5,y+0.5,z'],
            '66':['x,y,z',
                '-x,-y,z',
                '-x,y,-z+0.5',
                'x,-y,-z+0.5',
                '-x,-y,-z',
                'x,y,-z',
                'x,-y,z+0.5',
                '-x,y,z+0.5',
                'x+0.5,y+0.5,z',
                '-x+0.5,-y+0.5,z',
                '-x+0.5,y+0.5,-z+0.5',
                'x+0.5,-y+0.5,-z+0.5',
                '-x+0.5,-y+0.5,-z',
                'x+0.5,y+0.5,-z',
                'x+0.5,-y+0.5,z+0.5',
                '-x+0.5,y+0.5,z+0.5'],
            '67':['x,y,z',
                '-x,-y+0.5,z',
                '-x,y+0.5,-z',
                'x,-y,-z',
                '-x,-y,-z',
                'x,y+0.5,-z',
                'x,-y+0.5,z',
                '-x,y,z',
                'x+0.5,y+0.5,z',
                '-x+0.5,-y,z',
                '-x+0.5,y,-z',
                'x+0.5,-y+0.5,-z',
                '-x+0.5,-y+0.5,-z',
                'x+0.5,y,-z',
                'x+0.5,-y,z',
                '-x+0.5,y+0.5,z'],
            '68':['x,y,z',
                '-x+0.5,-y,z',
                '-x,y,-z+0.5',
                'x+0.5,-y,-z+0.5',
                '-x,-y,-z',
                'x+0.5,y,-z',
                'x,-y,z+0.5',
                '-x+0.5,y,z+0.5',
                'x+0.5,y+0.5,z',
                '-x,-y+0.5,z',
                '-x+0.5,y+0.5,-z+0.5',
                'x,-y+0.5,-z+0.5',
                '-x+0.5,-y+0.5,-z',
                'x,y+0.5,-z',
                'x+0.5,-y+0.5,z+0.5',
                '-x,y+0.5,z+0.5'],
            '69':['x,y,z',
                '-x,-y,z',
                '-x,y,-z',
                'x,-y,-z',
                '-x,-y,-z',
                'x,y,-z',
                'x,-y,z',
                '-x,y,z',
                'x,y+0.5,z+0.5',
                '-x,-y+0.5,z+0.5',
                '-x,y+0.5,-z+0.5',
                'x,-y+0.5,-z+0.5',
                '-x,-y+0.5,-z+0.5',
                'x,y+0.5,-z+0.5',
                'x,-y+0.5,z+0.5',
                '-x,y+0.5,z+0.5',
                'x+0.5,y,z+0.5',
                '-x+0.5,-y,z+0.5',
                '-x+0.5,y,-z+0.5',
                'x+0.5,-y,-z+0.5',
                '-x+0.5,-y,-z+0.5',
                'x+0.5,y,-z+0.5',
                'x+0.5,-y,z+0.5',
                '-x+0.5,y,z+0.5',
                'x+0.5,y+0.5,z',
                '-x+0.5,-y+0.5,z',
                '-x+0.5,y+0.5,-z',
                'x+0.5,-y+0.5,-z',
                '-x+0.5,-y+0.5,-z',
                'x+0.5,y+0.5,-z',
                'x+0.5,-y+0.5,z',
                '-x+0.5,y+0.5,z'],
            '70':['x,y,z',
                '-x+0.75,-y+0.75,z',
                '-x+0.75,y,-z+0.75',
                'x,-y+0.75,-z+0.75',
                '-x,-y,-z',
                'x+0.25,y+0.25,-z',
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			'P 21 m n':['x+.5, y+.5, -z',
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			'P b n 21':['-x+.5, y+.5, z',
				'x+.5, -y+.5, z+.5',
				'-x, -y, z+.5',
				'x, y, z'],
			'P c 21 n':['-x+.5, y, z+.5',
				'x+.5, y+.5, -z+.5',
				'-x, y+.5, -z',
				'x, y, z'],
			'P n 21 a':['x+.5, y, -z+.5',
				'-x+.5, y+.5, z+.5',
				'-x, y+.5, -z',
				'x, y, z'],
			'P 2 n n':['x+.5, -y+.5, z+.5',
				'x+.5, y+.5, -z+.5',
				'x, -y, -z',
				'x, y, z'],
			'P n 2 n':['x+.5, y+.5, -z+.5',
				'-x+.5, y+.5, z+.5',
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				'x, y, z'],
			'A 2 m m':['x, y, -z',
				'x, -y, z',
				'x, -y, -z',
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				'x, -y+.5, z+.5',
				'x, -y+.5, -z+.5',
				'x, y+.5, z+.5'],
			'B m 2 m':['x,y,z',
				'-x,y,-z',
				'x,y,-z',
				'-x,y,z',
				'x+1/2,y,z+1/2',
				'-x+1/2,y,-z+1/2',
				'x+1/2,y,-z+1/2',
				'-x+1/2,y,z+1/2'],
			'A 21 a m':['x+.5, -y, z',
				'x+.5, -y, -z',
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				'x+.5, -y+.5, -z+.5',
				'x, y+.5, -z+.5',
				'x, y+.5, z+.5'],
			'A 21 m a':['x+.5, y, -z',
				'x+.5, -y, -z',
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				'x+.5, -y+.5, -z+.5',
				'x, -y+.5, z+.5',
				'x, y+.5, z+.5'],
			'B b 21 m':['-x, y+.5, z',
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				'x+.5, y, -z+.5',
				'x+.5, y, z+.5'],
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				'-x,y+1/2,-z',
				'x,y+1/2,-z',
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				'x+1/2,y,z+1/2',
				'-x+1/2,y+1/2,-z+1/2',
				'x+1/2,y+1/2,-z+1/2',
				'-x+1/2,y,z+1/2'],
			'C c m 21':['-x, y, z+.5',
				'-x, -y, z+.5',
				'x, -y, z',
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				'x+.5, -y+.5, z',
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				'x+.5, y+.5, -z+.5',
				'x, -y+.5, -z+.5',
				'x, y+.5, z+.5'],
			'B b 2 b':['x, y+.5, -z',
				'-x, y+.5, z',
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				'x+.5, y, z+.5'],
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				'-x, y+.5, z+.5',
				'-x, y+.5, -z+.5',
				'x, y+.5, z+.5'],
			'B 2 m m':['x, y, -z',
				'x, -y, z',
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				'x+.5, -y, -z+.5',
				'x+.5, y, z+.5'],
			'B m m 2':['-x, y, z',
				'x, -y, z',
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				'x+.5, -y, z+.5',
				'-x+.5, -y, z+.5',
				'x+.5, y, z+.5'],
			'C 2 m m':['x, -y, z',
				'x, y, -z',
				'x, -y, -z',
				'x, y, z',
				'x+.5, -y+.5, z',
				'x+.5, y+.5, -z',
				'x+.5, -y+.5, -z',
				'x+.5, y+.5, z'],
			'C m 2 m':['-x, y, z',
				'x, y, -z',
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				'x+.5, y+.5, z'],
			'A b m 2':['x, -y+.5, z',
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				'x, y+.5, z+.5'],
			'A c 2 m':['x,y,z',
				'-x,y,-z',
				'x,y,-z+1/2',
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				'x,y+1/2,z+1/2',
				'-x,y+1/2,-z+1/2',
				'x,y+1/2,-z',
				'-x,y+1/2,z'],
			'B 2 c m':['x,y,z',
				'x,-y,-z',
				'x,y,-z+1/2',
				'x,-y,z+1/2',
				'x+1/2,y,z+1/2',
				'x+1/2,-y,-z+1/2',
				'x+1/2,y,-z',
				'x+1/2,-y,z'],
			'B m a 2':['x,y,z',
				'-x,-y,z',
				'-x+1/2,y,z',
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				'-x+1/2,-y,z+1/2',
				'-x,y,z+1/2',
				'x,-y,z+1/2'],
			'C 2 m b':['x, -y+.5, z',
				'x, y+.5, -z',
				'x, -y, -z',
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			'A m 2 a':['x,y,z',
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				'x+1/2,y,-z',
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				'-x,y+1/2,-z+1/2',
				'x+1/2,y+1/2,-z+1/2',
				'-x+1/2,y+1/2,z+1/2'],
			'B 2 m b':['x, y+.5, -z',
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				'x, -y, -z',
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				'x+.5, -y+.5, z+.5',
				'x+.5, -y, -z+.5',
				'x+.5, y, z+.5'],
			'B b m 2':['-x, y+.5, z',
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				'x+.5, -y+.5, z+.5',
				'-x+.5, -y, z+.5',
				'x+.5, y, z+.5'],
			'C 2 c m':['x, -y, z+.5',
				'x, y, -z+.5',
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				'x+.5, y+.5, -z+.5',
				'x+.5, -y+.5, -z',
				'x+.5, y+.5, z'],
			'C c 2 m':['-x, y, z+.5',
				'x, y, -z+.5',
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				'x+.5, y+.5, -z+.5',
				'-x+.5, y+.5, -z',
				'x+.5, y+.5, z'],
			'A b a 2':['x+.5, -y+.5, z',
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				'x, y+.5, z+.5'],
			'A c 2 a':['x,y,z',
				'-x,y,-z',
				'x+1/2,y,-z+1/2',
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				'x,y+1/2,z+1/2',
				'-x,y+1/2,-z+1/2',
				'x+1/2,y+1/2,-z',
				'-x+1/2,y+1/2,z'],
			'B 2 c b':['x, y+.5, -z+.5',
				'x, -y+.5, z+.5',
				'x, -y, -z',
				'x, y, z',
				'x+.5, y+.5, -z',
				'x+.5, -y+.5, z',
				'x+.5, -y, -z+.5',
				'x+.5, y, z+.5'],
			'B b a 2':['-x+.5, y+.5, z',
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				'x, -y+.5, z+.5',
				'-x+.5, -y, z+.5',
				'x+.5, y, z+.5'],
			'C 2 c b':['x, -y+.5, z+.5',
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				'x, -y, -z',
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				'x+.5, y, -z+.5',
				'x+.5, -y+.5, -z',
				'x+.5, y+.5, z'],
			'C c 2 a':['-x+.5, y, z+.5',
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				'x, y+.5, -z+.5',
				'-x+.5, y+.5, -z',
				'x+.5, y+.5, z'],
			'F 2 m m':['x, -y, z',
				'x, y, -z',
				'x, -y, -z',
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				'x+.5, -y, z+.5',
				'x+.5, -y+.5, z',
				'x, y+.5, -z+.5',
				'x+.5, y, -z+.5',
				'x+.5, y+.5, -z',
				'x, -y+.5, -z+.5',
				'x+.5, -y, -z+.5',
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				'x+.5, y, z+.5',
				'x+.5, y+.5, z'],
			'F m 2 m':['x, y, -z',
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				'x+.5, y, z+.5',
				'x+.5, y+.5, z'],
			'F 2 d d':['x+.25, -y+.25, z+.25',
				'x+.25, y+.25, -z+.25',
				'x, -y, -z',
				'x, y, z',
				'x+.25, -y+.75, z+.75',
				'x+.75, -y+.25, z+.75',
				'x+.75, -y+.75, z+.25',
				'x+.25, y+.75, -z+.75',
				'x+.75, y+.25, -z+.75',
				'x+.75, y+.75, -z+.25',
				'x, -y+.5, -z+.5',
				'x+.5, -y, -z+.5',
				'x+.5, -y+.5, -z',
				'x, y+.5, z+.5',
				'x+.5, y, z+.5',
				'x+.5, y+.5, z'],
			'F d 2 d':['x+.25, y+.25, -z+.25',
				'-x+.25, y+.25, z+.25',
				'-x, y, -z',
				'x, y, z',
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				'x+.75, y+.25, -z+.75',
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				'-x+.75, y+.25, z+.75',
				'-x+.75, y+.75, z+.25',
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				'x, y+.5, z+.5',
				'x+.5, y, z+.5',
				'x+.5, y+.5, z'],
			'I 2 m m':['x, -y, z',
				'x, y, -z',
				'x, -y, -z',
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				'x+.5, -y+.5, z+.5',
				'x+.5, y+.5, -z+.5',
				'x+.5, -y+.5, -z+.5',
				'x+.5, y+.5, z+.5'],
			'I m 2 m':['x, y, -z',
				'-x, y, z',
				'-x, y, -z',
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				'-x+.5, y+.5, z+.5',
				'-x+.5, y+.5, -z+.5',
				'x+.5, y+.5, z+.5'],
			'I 2 c b':['x,y,z',
				'x,-y,-z',
				'x,y+1/2,-z+1/2',
				'x,-y+1/2,z+1/2',
				'x+1/2,y+1/2,z+1/2',
				'x+1/2,-y+1/2,-z+1/2',
				'x+1/2,y,-z',
				'x+1/2,-y,z'],
			'I c 2 a':['x,y,z',
				'-x,y,-z',
				'x+1/2,y,-z+1/2',
				'-x+1/2,y,z+1/2',
				'x+1/2,y+1/2,z+1/2',
				'-x+1/2,y+1/2,-z+1/2',
				'x,y+1/2,-z',
				'-x,y+1/2,z'],
			'I 2 c m':['x, -y, z+.5',
				'x, y, -z+.5',
				'x, -y, -z',
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				'x+.5, y+.5, -z',
				'x+.5, -y+.5, -z+.5',
				'x+.5, y+.5, z+.5'],
			'I 2 m b':['x, y+.5, -z',
				'x, -y+.5, z',
				'x, -y, -z',
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				'x+.5, -y, z+.5',
				'x+.5, -y+.5, -z+.5',
				'x+.5, y+.5, z+.5'],
			'I b m 2':['-x, y+.5, z',
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				'x+.5, -y, z+.5',
				'-x+.5, -y+.5, z+.5',
				'x+.5, y+.5, z+.5'],
			'I 2 c m':['x, -y, z+.5',
				'x, y, -z+.5',
				'x, -y, -z',
				'x, y, z',
				'x+.5, -y+.5, z',
				'x+.5, y+.5, -z',
				'x+.5, -y+.5, -z+.5',
				'x+.5, y+.5, z+.5'],
			'I m 2 a':['x,y,z',
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				'x+1/2,y,-z',
				'-x+1/2,y,z',
				'x+1/2,y+1/2,z+1/2',
				'-x+1/2,y+1/2,-z+1/2',
				'x,y+1/2,-z+1/2',
				'-x,y+1/2,z+1/2'],
			'P b m b':['x,y,z',
				'-x,y,-z',
				'-x,-y+1/2,z',
				'x,-y+1/2,-z',
				'-x,-y,-z',
				'x,-y,z',
				'x,y+1/2,-z',
				'-x,y+1/2,z'],
			'P m a a':['x,y,z',
				'x,-y,-z',
				'-x+1/2,-y,z',
				'-x+1/2,y,-z',
				'-x,-y,-z',
				'-x,y,z',
				'x+1/2,y,-z',
				'x+1/2,-y,z'],
			'P b m m':['x, -y+.5, -z',
				'-x, y+.5, -z',
				'x, y, -z',
				'-x, -y, -z',
				'-x, y+.5, z',
				'x, -y+.5, z',
				'-x, -y, z',
				'x, y, z'],
			'P c m m':['x,y,z',
				'x,-y,-z+1/2',
				'-x,y,-z',
				'-x,-y,z+1/2',
				'-x,-y,-z',
				'-x,y,z+1/2',
				'x,-y,z',
				'x,y,-z+1/2'],
			'P m a m':['-x+.5, y, -z',
				'x+.5, -y, -z',
				'x, y, -z',
				'-x, -y, -z',
				'x+.5, -y, z',
				'-x+.5, y, z',
				'-x, -y, z',
				'x, y, z'],
			'P m c m':['-x, y, -z+.5',
				'-x, -y, z+.5',
				'-x, y, z',
				'-x, -y, -z',
				'x, -y, z+.5',
				'x, y, -z+.5',
				'x, -y, -z',
				'x, y, z'],
			'P m m b':['-x, -y+.5, z',
				'-x, y+.5, -z',
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				'x, y+.5, -z',
				'x, -y+.5, z',
				'x, -y, -z',
				'x, y, z'],
			'P b n n':['x+.5, y+.5, -z+.5',
				'x+.5, -y, z+.5',
				'-x, y+.5, z',
				'-x, -y, -z',
				'-x+.5, -y+.5, z+.5',
				'-x+.5, y, -z+.5',
				'x, -y+.5, -z',
				'x, y, z'],
			'P c n n':['x+.5, -y+.5, z+.5',
				'x+.5, y+.5, -z',
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				'-x, -y, -z',
				'-x+.5, y+.5, -z+.5',
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				'x, -y, -z+.5',
				'x, y, z'],
			'P n a n':['x+.5, y+.5, -z+.5',
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				'x+.5, -y, z',
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				'-x+.5, -y+.5, z+.5',
				'x, -y+.5, -z+.5',
				'-x+.5, y, -z',
				'x, y, z'],
			'P n c n':['-x+.5, y+.5, z+.5',
				'x+.5, y+.5, -z',
				'x, -y, z+.5',
				'-x, -y, -z',
				'x+.5, -y+.5, -z+.5',
				'-x+.5, -y+.5, z',
				'-x, y, -z+.5',
				'x, y, z'],
			'P n n b':['x,y,z',
				'-x,-y+1/2,z',
				'x+1/2,-y+1/2,-z+1/2',
				'-x+1/2,y,-z+1/2',
				'-x,-y,-z',
				'x,y+1/2,-z',
				'-x+1/2,y+1/2,z+1/2',
				'x+1/2,-y,z+1/2'],
			'P b m n':['-x+.5, y+.5, z',
				'x+.5, y+.5, -z',
				'x, -y, z',
				'-x, -y, -z',
				'x+.5, -y+.5, -z',
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				'-x, y, -z',
				'x, y, z'],
			'P c n m':['-x+.5, y, z+.5',
				'x+.5, -y, z+.5',
				'x, y, -z',
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				'x+.5, -y, -z+.5',
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				'-x, -y, z',
				'x, y, z'],
			'P m a n':['x+.5, -y+.5, z',
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				'x, -y, -z',
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				'-x, y+.5, -z',
				'-x, -y, z+.5',
				'-x, -y, -z',
				'x, -y+.5, -z+.5',
				'x, -y+.5, z',
				'x, y, -z+.5',
				'x, y, z'],
			'A b a a s':['x,y,z',
				'x,-y+1/2,-z+1/2',
				'-x,-y,z',
				'-x,y+1/2,-z+1/2',
				'-x+1/2,-y,-z+1/2',
				'-x+1/2,y+1/2,z',
				'x+1/2,y,-z+1/2',
				'x+1/2,-y+1/2,z',
				'x,y+1/2,z+1/2',
				'x,-y,-z',
				'-x,-y+1/2,z+1/2',
				'-x,y,-z',
				'-x+1/2,-y+1/2,-z',
				'-x+1/2,y,z+1/2',
				'x+1/2,y+1/2,-z',
				'x+1/2,-y,z+1/2'],
			'A b a a z':['x,y,z',
				'x,-y+1/2,-z',
				'-x+1/2,-y,z',
				'-x+1/2,y+1/2,-z',
				'-x,-y,-z',
				'-x,y+1/2,z',
				'x+1/2,y,-z',
				'x+1/2,-y+1/2,z',
				'x,y+1/2,z+1/2',
				'x,-y,-z+1/2',
				'-x+1/2,-y+1/2,z+1/2',
				'-x+1/2,y,-z+1/2',
				'-x,-y+1/2,-z+1/2',
				'-x,y,z+1/2',
				'x+1/2,y+1/2,-z+1/2',
				'x+1/2,-y,z+1/2'],
			'A c a a s':['x,y,z',
				'x,-y+1/2,-z+1/2',
				'-x,y,-z',
				'-x,-y+1/2,z+1/2',
				'-x+1/2,-y+1/2,-z',
				'-x+1/2,y,z+1/2',
				'x+1/2,-y+1/2,z',
				'x+1/2,y,-z+1/2',
				'x,y+1/2,z+1/2',
				'x,-y,-z',
				'-x,y+1/2,-z+1/2',
				'-x,-y,z',
				'-x+1/2,-y,-z+1/2',
				'-x+1/2,y+1/2,z',
				'x+1/2,-y,z+1/2',
				'x+1/2,y+1/2,-z'],
			'A c a a z':['x,y,z',
				'x,-y,-z+1/2',
				'-x+1/2,y,-z',
				'-x+1/2,-y,z+1/2',
				'-x,-y,-z',
				'-x,y,z+1/2',
				'x+1/2,-y,z',
				'x+1/2,y,-z+1/2',
				'x,y+1/2,z+1/2',
				'x,-y+1/2,-z',
				'-x+1/2,y+1/2,-z+1/2',
				'-x+1/2,-y+1/2,z',
				'-x,-y+1/2,-z+1/2',
				'-x,y+1/2,z',
				'x+1/2,-y+1/2,z+1/2',
				'x+1/2,y+1/2,-z'],
			'B b a b s':['x,y,z',
				'-x+1/2,y,-z+1/2',
				'-x,-y,z',
				'x+1/2,-y,-z+1/2',
				'-x,-y+1/2,-z+1/2',
				'x+1/2,-y+1/2,z',
				'x,y+1/2,-z+1/2',
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				'x+1/2,y,z+1/2',
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				'-x+1/2,-y+1/2,-z',
				'x,-y+1/2,z+1/2',
				'x+1/2,y+1/2,-z',
				'-x,y+1/2,z+1/2'],
			'B b a b z':['x, -y, z+.5',
				'-x+.5, -y+.5, z+.5',
				'x+.5, -y+.5, -z',
				'-x, -y, -z',
				'-x, y, -z+.5',
				'x+.5, y+.5, -z+.5',
				'-x+.5, y+.5, z',
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				'-x+.5, -y, -z+.5',
				'-x+.5, y, -z',
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				'x+.5, y, z+.5'],
			'B b c b s':['x,y,z',
				'-x+1/2,y,-z+1/2',
				'x,-y,-z',
				'-x+1/2,-y,z+1/2',
				'-x+1/2,-y+1/2,-z',
				'x,-y+1/2,z+1/2',
				'-x+1/2,y+1/2,z',
				'x,y+1/2,-z+1/2',
				'x+1/2,y,z+1/2',
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				'x+1/2,-y,-z+1/2',
				'-x,-y,z',
				'-x,-y+1/2,-z+1/2',
				'x+1/2,-y+1/2,z',
				'-x,y+1/2,z+1/2',
				'x+1/2,y+1/2,-z'],
			'B b c b z':['x+.5, -y, z',
				'x+.5, -y+.5, -z+.5',
				'-x, -y+.5, z+.5',
				'-x, -y, -z',
				'-x+.5, y, -z',
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				'x, -y+.5, -z',
				'-x+.5, -y+.5, z',
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				'-x, y, -z+.5',
				'-x, y+.5, z',
				'x+.5, y+.5, -z',
				'x+.5, y, z+.5'],
			'C c c a s':['-x+.5, y, z+.5',
				'x, -y+.5, z+.5',
				'x+.5, y, -z+.5',
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				'x+.5, -y+.5, -z',
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				'x, -y, -z',
				'-x+.5, y+.5, -z',
				'-x, -y, z',
				'x+.5, y+.5, z'],
			'C c c a z':['x, y+.5, -z',
				'-x+.5, y+.5, -z+.5',
				'x+.5, -y, -z+.5',
				'-x, -y, -z',
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				'x, -y+.5, -z+.5',
				'-x+.5, -y+.5, -z',
				'-x+.5, -y, z',
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				'-x, y+.5, z+.5',
				'x+.5, y+.5, z'],
			'C c c b s':['x,y,z',
				'-x+1/2,-y+1/2,z',
				'x,-y,-z',
				'-x+1/2,y+1/2,-z',
				'-x+1/2,-y,-z+1/2',
				'x,y+1/2,-z+1/2',
				'-x+1/2,y,z+1/2',
				'x,-y+1/2,z+1/2',
				'x+1/2,y+1/2,z',
				'-x,-y,z',
				'x+1/2,-y+1/2,-z',
				'-x,y,-z',
				'-x,-y+1/2,-z+1/2',
				'x+1/2,y,-z+1/2',
				'-x,y+1/2,z+1/2',
				'x+1/2,-y,z+1/2'],
			'C c c b z':['x,y,z',
				'-x,-y+1/2,z',
				'x,-y,-z+1/2',
				'-x,y+1/2,-z+1/2',
				'-x,-y,-z',
				'x,y+1/2,-z',
				'-x,y,z+1/2',
				'x,-y+1/2,z+1/2',
				'x+1/2,y+1/2,z',
				'-x+1/2,-y,z',
				'x+1/2,-y+1/2,-z+1/2',
				'-x+1/2,y,-z+1/2',
				'-x+1/2,-y+1/2,-z',
				'x+1/2,y,-z',
				'-x+1/2,y+1/2,z+1/2',
				'x+1/2,-y,z+1/2'],
			'C c c e s':['-x+.5, y, z+.5',
				'x, -y+.5, z+.5',
				'x+.5, y, -z+.5',
				'-x, -y+.5, -z+.5',
				'x+.5, -y+.5, -z',
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				'-x+.5, -y+.5, z',
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				'x+.5, -y, z+.5',
				'x, y+.5, -z+.5',
				'-x+.5, -y, -z+.5',
				'x, -y, -z',
				'-x+.5, y+.5, -z',
				'-x, -y, z',
				'x+.5, y+.5, z'],
			'F d d d s':['x+.25, y+.25, -z+.25',
				'-x+.25, y+.25, z+.25',
				'-x, -y, z',
				'x, -y, -z',
				'x+.25, -y+.25, z+.25',
				'-x+.25, -y+.25, -z+.25',
				'-x, y, -z',
				'x, y, z',
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				'x+.75, y+.25, -z+.75',
				'x+.75, y+.75, -z+.25',
				'-x+.25, y+.75, z+.75',
				'-x+.75, y+.25, z+.75',
				'-x+.75, y+.75, z+.25',
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				'-x+.5, -y, z+.5',
				'-x+.5, -y+.5, z',
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				'x+.5, -y+.5, -z',
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				'x+.75, -y+.25, z+.75',
				'x+.75, -y+.75, z+.25',
				'-x+.25, -y+.75, -z+.75',
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				'-x+.5, y, -z+.5',
				'-x+.5, y+.5, -z',
				'x, y+.5, z+.5',
				'x+.5, y, z+.5',
				'x+.5, y+.5, z'],
			'F d d d z':['x+.75, y+.75, -z',
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				'-x, y+.75, z+.75',
				'-x, -y, -z',
				'-x+.25, -y+.25, z',
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				'x+.5, y+.5, z'],
			'P 42/n s':['y+.5, -x+.5, z+.5',
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				'x+.5, y+.5, -z+.5',
				'-x, -y, z',
				'x, y, z'],
			'P 42/n z':['-y+.5, x, -z+.5',
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				'x+.5, y+.5, -z',
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				'x, y, z'],
			'P 4/n s':['y+.5, -x+.5, z',
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			'P 4/n z':['-y, x+.5, -z',
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				'-y+.5, x, z',
				'-x+.5, -y+.5, z',
				'x, y, z'],
			'I 41/a s':['y, -x+.5, z+.25',
				'-y, x+.5, z+.25',
				'y, -x, -z',
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				'x+.5, y, -z+.75',
				'-x+.5, -y+.5, z+.5',
				'x+.5, y+.5, z+.5'],
			'I 41/a z':['-y+.75, x+.75, -z+.75',
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				'x+.5, y+.5, z+.5'],
			'P 4/n b m s':['y+.5, x+.5, z',
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			'P 4/n b m z':['y+.5, x+.5, z',
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			'P 4/n n c s':['y+.5, x+.5, z+.5',
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			'P 4/n n c z':['-y, x+.5, -z',
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			'P 4/n m m s':['-y+.5, -x+.5, z',
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			'P 4/n c c s':['y+.5, x+.5, z+.5',
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			'P 4/n c c z':['y+.5, x+.5, -z+.5',
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			'P 42/n b c s':['y+.5, -x+.5, z+.5',
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			'P 42/n b c z':['y, x, -z+.5',
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			'P 42/n n m s':['-y+.5, -x+.5, -z+.5',
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				'x, x-y, z',
				'-y, -x, z',
				'-x+y, -x, z',
				'-y, x-y, z',
				'x, y, z',
				'-x+y+.3333, y+.6666, z+.3333',
				'-x+y+.6666, y+.3333, z+.6666',
				'x+.3333, x-y+.6666, z+.3333',
				'x+.6666, x-y+.3333, z+.6666',
				'-y+.3333, -x+.6666, z+.3333',
				'-y+.6666, -x+.3333, z+.6666',
				'-x+y+.3333, -x+.6666, z+.3333',
				'-x+y+.6666, -x+.3333, z+.6666',
				'-y+.3333, x-y+.6666, z+.3333',
				'-y+.6666, x-y+.3333, z+.6666',
				'x+.3333, y+.6666, z+.3333',
				'x+.6666, y+.3333, z+.6666'],
			'R 3 m r':['z, y, x',
				'z, x, y',
				'x, z, y',
				'y, z, x',
				'y, x, z',
				'x, y, z'],
			'R 3 c h':['-x+y, y, z+.5',
				'x, x-y, z+.5',
				'-y, -x, z+.5',
				'-x+y, -x, z',
				'-y, x-y, z',
				'x, y, z',
				'-x+y+.6666, y+.3333, z+.8333',
				'-x+y+.3333, y+.6666, z+.1666',
				'x+.6666, x-y+.3333, z+.8333',
				'x+.3333, x-y+.6666, z+.1666',
				'-y+.6666, -x+.3333, z+.8333',
				'-y+.3333, -x+.6666, z+.1666',
				'-x+y+.6666, -x+.3333, z+.3333',
				'-x+y+.3333, -x+.6666, z+.6666',
				'-y+.6666, x-y+.3333, z+.3333',
				'-y+.3333, x-y+.6666, z+.6666',
				'x+.6666, y+.3333, z+.3333',
				'x+.3333, y+.6666, z+.6666'],
			'R 3 c r':['z+.5, y+.5, x+.5',
				'z, x, y',
				'x+.5, z+.5, y+.5',
				'y, z, x',
				'y+.5, x+.5, z+.5',
				'x, y, z'],
			'R -3 m h':['x-y, -y, -z',
				'-x, -x+y, -z',
				'y, x, -z',
				'x-y, x, -z',
				'y, -x+y, -z',
				'-x, -y, -z',
				'-x+y, y, z',
				'x, x-y, z',
				'-y, -x, z',
				'-x+y, -x, z',
				'-y, x-y, z',
				'x, y, z',
				'x-y+.6666, -y+.3333, -z+.3333',
				'x-y+.3333, -y+.6666, -z+.6666',
				'-x+.6666, -x+y+.3333, -z+.3333',
				'-x+.3333, -x+y+.6666, -z+.6666',
				'y+.6666, x+.3333, -z+.3333',
				'y+.3333, x+.6666, -z+.6666',
				'x-y+.6666, x+.3333, -z+.3333',
				'x-y+.3333, x+.6666, -z+.6666',
				'y+.6666, -x+y+.3333, -z+.3333',
				'y+.3333, -x+y+.6666, -z+.6666',
				'-x+.6666, -y+.3333, -z+.3333',
				'-x+.3333, -y+.6666, -z+.6666',
				'-x+y+.6666, y+.3333, z+.3333',
				'-x+y+.3333, y+.6666, z+.6666',
				'x+.6666, x-y+.3333, z+.3333',
				'x+.3333, x-y+.6666, z+.6666',
				'-y+.6666, -x+.3333, z+.3333',
				'-y+.3333, -x+.6666, z+.6666',
				'-x+y+.6666, -x+.3333, z+.3333',
				'-x+y+.3333, -x+.6666, z+.6666',
				'-y+.6666, x-y+.3333, z+.3333',
				'-y+.3333, x-y+.6666, z+.6666',
				'x+.6666, y+.3333, z+.3333',
				'x+.3333, y+.6666, z+.6666'],
			'R -3 m hr':['x-y, -y, -z',
				'-x, -x+y, -z',
				'y, x, -z',
				'x-y, x, -z',
				'y, -x+y, -z',
				'-x, -y, -z',
				'-x+y, y, z',
				'x, x-y, z',
				'-y, -x, z',
				'-x+y, -x, z',
				'-y, x-y, z',
				'x, y, z',
				'x-y+.3333, -y+.6666, -z+.3333',
				'x-y+.6666, -y+.3333, -z+.6666',
				'-x+.3333, -x+y+.6666, -z+.3333',
				'-x+.6666, -x+y+.3333, -z+.6666',
				'y+.3333, x+.6666, -z+.3333',
				'y+.6666, x+.3333, -z+.6666',
				'x-y+.3333, x+.6666, -z+.3333',
				'x-y+.6666, x+.3333, -z+.6666',
				'y+.3333, -x+y+.6666, -z+.3333',
				'y+.6666, -x+y+.3333, -z+.6666',
				'-x+.3333, -y+.6666, -z+.3333',
				'-x+.6666, -y+.3333, -z+.6666',
				'-x+y+.3333, y+.6666, z+.3333',
				'-x+y+.6666, y+.3333, z+.6666',
				'x+.3333, x-y+.6666, z+.3333',
				'x+.6666, x-y+.3333, z+.6666',
				'-y+.3333, -x+.6666, z+.3333',
				'-y+.6666, -x+.3333, z+.6666',
				'-x+y+.3333, -x+.6666, z+.3333',
				'-x+y+.6666, -x+.3333, z+.6666',
				'-y+.3333, x-y+.6666, z+.3333',
				'-y+.6666, x-y+.3333, z+.6666',
				'x+.3333, y+.6666, z+.3333',
				'x+.6666, y+.3333, z+.6666'],
			'R -3 m r':['-z, -y, -x',
				'-z, -x, -y',
				'-x, -z, -y',
				'-y, -z, -x',
				'-y, -x, -z',
				'-x, -y, -z',
				'z, y, x',
				'z, x, y',
				'x, z, y',
				'y, z, x',
				'y, x, z',
				'x, y, z'],
			'R -3 c h':['x-y, -y, -z+.5',
				'-x, -x+y, -z+.5',
				'y, x, -z+.5',
				'x-y, x, -z',
				'y, -x+y, -z',
				'-x, -y, -z',
				'-x+y, y, z+.5',
				'x, x-y, z+.5',
				'-y, -x, z+.5',
				'-x+y, -x, z',
				'-y, x-y, z',
				'x, y, z',
				'x-y+.6666, -y+.3333, -z+.8333',
				'x-y+.3333, -y+.6666, -z+.1666',
				'-x+.6666, -x+y+.3333, -z+.8333',
				'-x+.3333, -x+y+.6666, -z+.1666',
				'y+.6666, x+.3333, -z+.8333',
				'y+.3333, x+.6666, -z+.1666',
				'x-y+.6666, x+.3333, -z+.3333',
				'x-y+.3333, x+.6666, -z+.6666',
				'y+.6666, -x+y+.3333, -z+.3333',
				'y+.3333, -x+y+.6666, -z+.6666',
				'-x+.6666, -y+.3333, -z+.3333',
				'-x+.3333, -y+.6666, -z+.6666',
				'-x+y+.6666, y+.3333, z+.8333',
				'-x+y+.3333, y+.6666, z+.1666',
				'x+.6666, x-y+.3333, z+.8333',
				'x+.3333, x-y+.6666, z+.1666',
				'-y+.6666, -x+.3333, z+.8333',
				'-y+.3333, -x+.6666, z+.1666',
				'-x+y+.6666, -x+.3333, z+.3333',
				'-x+y+.3333, -x+.6666, z+.6666',
				'-y+.6666, x-y+.3333, z+.3333',
				'-y+.3333, x-y+.6666, z+.6666',
				'x+.6666, y+.3333, z+.3333',
				'x+.3333, y+.6666, z+.6666'],
			'R -3 c r':['-x+.5, -z+.5, -y+.5',
				'-z+.5, -y+.5, -x+.5',
				'-y+.5, -x+.5, -z+.5',
				'x+.5, z+.5, y+.5',
				'z+.5, y+.5, x+.5',
				'y+.5, x+.5, z+.5',
				'-z, -x, -y',
				'-y, -z, -x',
				'-x, -y, -z',
				'z, x, y',
				'y, z, x',
				'x, y, z']
            }