{"id":"https://openalex.org/W7158250386","doi":"https://doi.org/10.48550/arxiv.2604.25695","title":"Point Group Symmetry of Polyhedral Diagrams in Graphic Statics","display_name":"Point Group Symmetry of Polyhedral Diagrams in Graphic Statics","publication_year":2026,"publication_date":"2026-04-28","ids":{"openalex":"https://openalex.org/W7158250386","doi":"https://doi.org/10.48550/arxiv.2604.25695"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.25695","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.25695","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.25695","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113163008","display_name":"Yefan Zhi","orcid":"https://orcid.org/0000-0003-1654-4865"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhi, Yefan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134827139","display_name":"Yao Lu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lu, Yao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5066044280","display_name":"Masoud Akbarzadeh","orcid":"https://orcid.org/0000-0002-6402-615X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Akbarzadeh, Masoud","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11887","display_name":"Quasicrystal Structures and Properties","score":0.18129999935626984,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11887","display_name":"Quasicrystal Structures and Properties","score":0.18129999935626984,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13518","display_name":"Architecture and Computational Design","score":0.16660000383853912,"subfield":{"id":"https://openalex.org/subfields/2216","display_name":"Architecture"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10672","display_name":"Design Education and Practice","score":0.11540000140666962,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/symmetry-operation","display_name":"Symmetry operation","score":0.6834999918937683},{"id":"https://openalex.org/keywords/symmetry-group","display_name":"Symmetry group","score":0.5810999870300293},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.5328999757766724},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5134000182151794},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4323999881744385},{"id":"https://openalex.org/keywords/point-group","display_name":"Point group","score":0.43209999799728394},{"id":"https://openalex.org/keywords/rotational-symmetry","display_name":"Rotational symmetry","score":0.35269999504089355},{"id":"https://openalex.org/keywords/polyhedron","display_name":"Polyhedron","score":0.3424000144004822},{"id":"https://openalex.org/keywords/one-dimensional-symmetry-group","display_name":"One-dimensional symmetry group","score":0.3402000069618225},{"id":"https://openalex.org/keywords/group-theory","display_name":"Group theory","score":0.33980000019073486}],"concepts":[{"id":"https://openalex.org/C5534955","wikidata":"https://www.wikidata.org/wiki/Q7661343","display_name":"Symmetry operation","level":3,"score":0.6834999918937683},{"id":"https://openalex.org/C44306375","wikidata":"https://www.wikidata.org/wiki/Q902019","display_name":"Symmetry group","level":2,"score":0.5810999870300293},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.5328999757766724},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5134000182151794},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5060999989509583},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4323999881744385},{"id":"https://openalex.org/C57796230","wikidata":"https://www.wikidata.org/wiki/Q899720","display_name":"Point group","level":2,"score":0.43209999799728394},{"id":"https://openalex.org/C33026886","wikidata":"https://www.wikidata.org/wiki/Q593950","display_name":"Rotational symmetry","level":2,"score":0.35269999504089355},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3456999957561493},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.3424000144004822},{"id":"https://openalex.org/C164772539","wikidata":"https://www.wikidata.org/wiki/Q7092304","display_name":"One-dimensional symmetry group","level":3,"score":0.3402000069618225},{"id":"https://openalex.org/C81651864","wikidata":"https://www.wikidata.org/wiki/Q874429","display_name":"Group theory","level":2,"score":0.33980000019073486},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.3303000032901764},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.32820001244544983},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.32739999890327454},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.32249999046325684},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.3224000036716461},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3172000050544739},{"id":"https://openalex.org/C22511879","wikidata":"https://www.wikidata.org/wiki/Q7661339","display_name":"Symmetry number","level":5,"score":0.31630000472068787},{"id":"https://openalex.org/C35441770","wikidata":"https://www.wikidata.org/wiki/Q169019","display_name":"Statics","level":2,"score":0.3075000047683716},{"id":"https://openalex.org/C133978748","wikidata":"https://www.wikidata.org/wiki/Q15955882","display_name":"Reflection symmetry","level":2,"score":0.29580000042915344},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2955999970436096},{"id":"https://openalex.org/C205711294","wikidata":"https://www.wikidata.org/wiki/Q176953","display_name":"Rendering (computer graphics)","level":2,"score":0.2851000130176544},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.27970001101493835},{"id":"https://openalex.org/C203992732","wikidata":"https://www.wikidata.org/wiki/Q1066315","display_name":"Crystallographic point group","level":3,"score":0.27630001306533813},{"id":"https://openalex.org/C192423722","wikidata":"https://www.wikidata.org/wiki/Q1455736","display_name":"Global symmetry","level":4,"score":0.26930001378059387},{"id":"https://openalex.org/C188374626","wikidata":"https://www.wikidata.org/wiki/Q5914418","display_name":"Mirror symmetry","level":2,"score":0.2687000036239624},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2630000114440918},{"id":"https://openalex.org/C2776394503","wikidata":"https://www.wikidata.org/wiki/Q5282063","display_name":"Discrete symmetry","level":3,"score":0.26249998807907104},{"id":"https://openalex.org/C88548561","wikidata":"https://www.wikidata.org/wiki/Q347599","display_name":"sort","level":2,"score":0.26159998774528503},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.2612000107765198},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.26089999079704285},{"id":"https://openalex.org/C161085987","wikidata":"https://www.wikidata.org/wiki/Q2017567","display_name":"Octahedral symmetry","level":3,"score":0.2556999921798706},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.2531999945640564}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.25695","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.25695","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.25695","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.25695","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Symmetry":[0],"is":[1,163,196,208,230],"an":[2,50,102],"implicit":[3],"objective":[4],"in":[5,22,108,131,232],"structural":[6],"form-finding":[7,57],"that":[8,43,184,197],"often":[9],"reconciles":[10],"efficiency":[11],"and":[12,30,38,52,98,114,139,157,174,187,216,239],"aesthetics.":[13],"This":[14,206],"paper":[15,94,182],"identifies":[16],"the":[17,36,56,75,78,83,112,127,132,141,150,167,181,185,192,203,211,222,225,233],"symmetry":[18,76,96,113,130,144,152,195,219],"of":[19,40,58,77,119,129,135,143,170,200,214,224],"polyhedral":[20,41,137,172],"diagrams":[21,42,65],"three-dimensional":[23],"graphic":[24],"statics":[25],"(3DGS)":[26],"as":[27,33],"point":[28,100,168,193],"groups":[29],"formulates":[31],"them":[32],"constraints,":[34],"enabling":[35],"optimization":[37],"manipulation":[39],"preserve":[44],"such":[45],"symmetry.":[46],"3DGS":[47,215],"has":[48,202],"been":[49],"efficient":[51],"effective":[53],"tool":[54,105],"for":[55,66,86,190,237],"funicular":[59],"structures.":[60],"However,":[61],"when":[62],"modifying":[63],"complex":[64],"design":[67,80],"exploration":[68],"or":[69],"optimization,":[70],"one":[71],"can":[72],"easily":[73],"break":[74],"reciprocal":[79],"input,":[81],"rendering":[82],"result":[84],"undesirable":[85],"practical":[87],"use.":[88],"To":[89],"address":[90],"this":[91,93],"problem,":[92],"investigates":[95],"transformations":[97],"introduces":[99],"groups,":[101],"abstract":[103],"algebra":[104],"commonly":[106],"used":[107],"crystallography":[109],"to":[110,165],"represent":[111],"equivalence":[115],"between":[116],"a":[117,136,159,171],"network":[118],"atoms":[120],"(points":[121],"with":[122,210],"labels).":[123],"It":[124],"then":[125],"discusses":[126],"hierarchy":[128],"geometry":[133],"types":[134],"diagram,":[138],"proposes":[140],"constraint":[142,207],"through":[145],"edge":[146],"lengths.":[147],"Based":[148],"on":[149],"crystal":[151],"search":[153],"algorithm":[154,162],"by":[155],"spglib":[156],"pymatgen,":[158],"fast":[160],"fingerprinting":[161],"developed":[164],"identify":[166],"group":[169,194],"diagram":[173],"sort":[175],"equivalent":[176],"edges":[177,201],"into":[178],"sets.":[179],"Finally,":[180],"shows":[183],"necessary":[186],"sufficient":[188],"condition":[189],"preserving":[191],"each":[198],"set":[199],"same":[204],"length.":[205],"compatible":[209],"algebraic":[212],"formulation":[213],"effectively":[217],"preserves":[218],"while":[220],"reducing":[221],"dimension":[223],"solution":[226],"space.":[227],"The":[228],"method":[229],"implemented":[231],"PolyFrame":[234],"2":[235],"plug-in":[236],"Rhino":[238],"Grasshopper.":[240]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-04-30T00:00:00"}