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"equivalent_words": [ "aadaBd", "aadBad", "aaBadB", "aaBdaB", "acBaBB", "acBBcB", "addadC", "addaCd", "adCddC", "aBcaBB", "aBcBBc", "aCddCd", "bdCbCC", "bdCCdC", "bCdbCC", "bCdCCd" ] }, { "id": "geo-071", "word": "abcBad", "inverse_word": "DAbCBA", "word_length": 6, "trace": -107.740115370178, "trace_abs": 107.740115370178, "length": 9.359271657904, "matrix": { "a": { "re": -53.870057685089, "im": -76.183766184074 }, "b": { "re": -50.585208054802, "im": -78.396977435592 } }, "fixed_points": [ [ -0.999102370149, -0.042360995768 ], [ -0.373123190688, 0.927781808709 ] ], "primitive": true, "symmetry_multiplicity": 16, "equivalent_words": [ "abcBad", "abcDcB", "abADcD", "abCbAD", "adaBcb", "adcbCd", "adABcB", "adCbcd", "adCbCD", "adCdAB", "adCDaB", "aBaDCd", "aBcDcb", "aBcDCB", "aBCDcB", "aDCbCd" ] }, { "id": "geo-072", "word": "abdaBc", "inverse_word": "CbADBA", "word_length": 6, "trace": -107.740115370178, "trace_abs": 107.740115370178, "length": 9.359271657904, "matrix": { "a": { "re": 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"trace": 114.568542494924, "trace_abs": 114.568542494924, "length": 9.482194149272, "matrix": { "a": { "re": 57.284271247462, "im": 192.16652224137 }, "b": { "re": 54.336350255768, "im": 193.018188375029 } }, "fixed_points": [ [ -0.845083101067, 0.53463497107 ], [ -0.999883554551, -0.015260319106 ] ], "primitive": true, "symmetry_multiplicity": 4, "equivalent_words": [ "aadCCd", "aaBccB", "addaBB", "bbCddC" ] }, { "id": "geo-075", "word": "acadCd", "inverse_word": "DcDACA", "word_length": 6, "trace": 114.568542494924, "trace_abs": 114.568542494924, "length": 9.482194149272, "matrix": { "a": { "re": 57.284271247462, "im": 152.367532368147 }, "b": { "re": 43.726517905777, "im": 156.793954871184 } }, "fixed_points": [ [ -0.807124220219, 0.590381650406 ], [ -0.996166089769, -0.08748212157 ] ], "primitive": true, "symmetry_multiplicity": 8, "equivalent_words": [ "acadCd", "acDADc", "adaBDB", "adbdaB", "aBcAcB", "aBcBaC", "bCdBdC", "bCdCbD" ] }, { "id": "geo-076", "word": "acBcaB", "inverse_word": "bACbCA", "word_length": 6, "trace": 114.568542494924, "trace_abs": 114.568542494924, "length": 9.482194149272, "matrix": { "a": { "re": 57.284271247462, "im": -112.568542494924 }, "b": { "re": 69.340919059631, "im": -105.565152563476 } }, "fixed_points": [ [ -0.495968846848, -0.868340315174 ], [ -0.993899862623, -0.110286277828 ] ], "primitive": true, "symmetry_multiplicity": 4, "equivalent_words": [ "acBcaB", "adaCdC", "adBaBd", "bdCdbC" ] }, { "id": "geo-077", "word": "aacd", "inverse_word": "DCAA", "word_length": 4, "trace": 117.39696961967, "trace_abs": 117.39696961967, "length": 9.530977057139, "matrix": { "a": { "re": 58.698484809835, "im": 132.468037431535 }, "b": { "re": 58.087492456734, "im": 132.73332769136 } }, "fixed_points": [ [ -0.675189242946, 0.737644552756 ], [ -0.999989678274, -0.004543494849 ] ], "primitive": true, "symmetry_multiplicity": 16, "equivalent_words": [ "aacd", "aadc", "aaBC", "aaCB", "abdd", "abCC", "accD", "addb", "aBBD", "aCCb", "aDcc", "aDBB", "bbCD", "bbDC", "bcDD", "bDDc" ] }, { "id": "geo-078", "word": "abadC", "inverse_word": "cDABA", "word_length": 5, "trace": -117.39696961967, "trace_abs": 117.39696961967, "length": 9.530977057139, "matrix": { "a": { "re": -58.698484809835, "im": 84.426406871193 }, "b": { "re": -61.838634657699, "im": 82.148119636558 } }, "fixed_points": [ [ -0.999285649139, -0.037791420001 ], [ -0.312718493347, -0.949845852714 ] ], "primitive": true, "symmetry_multiplicity": 16, "equivalent_words": [ "abadC", "abaCd", "abdCb", "abCdb", "acdcB", "acBaD", "adcdB", "adBCB", "adCBC", "aBcaD", "aBcdc", "aBdcd", "aBCBd", "aCBCd", "aDcBD", "aDBcD" ] }, { "id": "geo-079", "word": "abAbd", "inverse_word": "DBaBA", "word_length": 5, "trace": 117.39696961967, "trace_abs": 117.39696961967, "length": 9.530977057139, "matrix": { "a": { "re": 58.698484809835, "im": 119.39696961967 }, "b": { "re": 52.782576281738, "im": 122.123495341369 } }, "fixed_points": [ [ -0.648772391294, 0.760982512476 ], [ -0.998804213511, -0.048889089502 ] ], "primitive": true, "symmetry_multiplicity": 16, "equivalent_words": [ "abAbd", "abCaB", "acDad", "acDcd", "adaDc", "adbAb", "adbAd", "adcDc", "adAbd", "aBaCb", "aBCbC", "aCbCB", "bcDbC", "bCbDc", "bCDcD", "bDcDC" ] }, { "id": "geo-080", "word": "aabd", "inverse_word": "DBAA", "word_length": 4, "trace": 124.225396744416, "trace_abs": 124.225396744416, "length": 9.644065648625, "matrix": { "a": { "re": 62.112698372208, "im": 131.053823869162 }, "b": { "re": 61.838634657699, "im": 131.17955371733 } }, "fixed_points": [ [ -0.634797311667, 0.772678699785 ], [ -0.999997941929, -0.002028826672 ] ], "primitive": true, "symmetry_multiplicity": 16, "equivalent_words": [ "aabd", "aadb", "aaBD", "aaDB", "abbC", "acdd", "acDD", "addc", "aBBC", "aCbb", "aCBB", "aDDc", "bccD", "bCCD", "bDcc", "bDCC" ] } ], "enumeration": { "method": "local enumeration of primitive cyclically reduced words, condensed by regular-polygon dihedral symmetries", "max_word_length": 6, "retained_shortest": 80, "raw_primitive_conjugacy_classes": 11818, "symmetry_orbits_before_limit": 890, "generated_by": "scripts/generate_hyperbolic_octagon_geodesics.py" } }