# list manipulation – Delete Duplicates by a distance test

Consider the following list which is of length 245:

``````list = {{1.7821782709267973`, 1.782178215568537`,
1.7821780839683263`}, {4.632562813287688`, 1.1067577689655785`,
1.087587771271402`}, {4.627734232255028`, 1.1069014595131055`,
1.0777279595894613`}, {4.6317308706419995`, 1.096541756979757`,
1.0961872811010953`}, {4.632423981962563`, 1.097190827117355`,
1.0969249027547516`}, {4.627963538705377`, 1.0926238830181279`,
1.0925706503230255`}, {4.629816058992955`, 1.0944778417527588`,
1.0944219685928114`}, {4.630612831346933`, 1.0952752844991205`,
1.095216675396808`}, {4.634369193140795`, 1.099471779954157`,
1.09853200574019`}, {1.7821782241937663`, 1.7821782217911688`,
1.782178218526167`}, {4.634250830189511`, 1.1019074843793748`,
1.096292161872628`}, {4.634231247683334`, 1.1010878292010011`,
1.0966391582638046`}, {4.633702274723675`, 1.0991852018078798`,
1.0974868921137435`}, {4.629831492511016`, 1.0945415201911441`,
1.0943893264761089`}, {4.631199467390834`, 1.0958629597045486`,
1.0958021208248092`}, {4.632889690506627`, 1.0959836253056743`,
1.0959817050980738`}, {4.633748366417633`, 1.0996015331220048`,
1.0971626432790218`}, {1.7821782258644072`, 1.782178213053708`,
1.7821782056997435`}, {1.7821782622464275`, 1.7821781764107172`,
1.7821781718676413`}, {4.634563055776168`, 1.0995031878511892`,
1.0988903915925954`}, {4.632746492697089`, 1.0975933124396806`,
1.0971173683833484`}, {4.6289921590805445`, 1.093693498426831`,
1.093558506242173`}, {4.628566772191042`, 1.093216332892832`,
1.0931826790306771`}, {4.6295627390486445`, 1.093862122711905`,
1.0937220515467836`}, {4.628484388976073`, 1.0931285780202415`,
1.0931054586574926`}, {4.631687966005123`, 1.0981088040442486`,
1.0945316912309686`}, {4.634659639818005`, 1.102861367265082`,
1.0941896180180226`}, {4.630986996972632`, 1.0976195839502099`,
1.0936203359565297`}, {4.633886353529327`, 1.0987969596238771`,
1.0982439889789972`}, {4.626854116741907`, 1.0915205867789937`,
1.0914561287134772`}, {4.631579419473298`, 1.0964131431992172`,
1.096012759191009`}, {4.63300410994884`, 1.0993298751859482`,
1.0959448855222167`}, {4.634665229125501`, 1.0993124890086887`,
1.0992856766088182`}, {4.6316675334667785`, 1.0991172713466837`,
1.0967786484022302`}, {4.633024264409726`, 1.0976822496790661`,
1.0975824300326498`}, {4.6103206892361825`, 1.0722185419416488`,
1.0655683869514032`}, {4.619138406225702`, 1.089874272371105`,
1.0776522988896653`}, {4.633253807856525`, 1.0992643110098186`,
1.0948888568188795`}, {4.634587401632189`, 1.1007410828610376`,
1.0976981625199784`}, {4.630549847946725`, 1.0956511288417514`,
1.0947161132035614`}, {4.6338761030110405`, 1.0985188725008304`,
1.098499636881484`}, {4.62647358589989`, 1.091203765090824`,
1.0910124861588886`}, {4.633606619785303`, 1.0983652466123346`,
1.0980204628746342`}, {4.63003015660613`, 1.094894235026198`,
1.0944318048050408`}, {1.7821782665598649`, 1.7821781910613592`,
1.7821781458443935`}, {1.782178262555449`, 1.7821782115531855`,
1.7821781281225377`}, {4.633878705367475`, 1.0987733497370047`,
1.098250192548254`}, {4.634111858237305`, 1.0990442063497432`,
1.0984478129803492`}, {4.628879612069581`, 1.0935157658501131`,
1.0935122142528435`}, {4.629931558657129`, 1.094615983482181`,
1.094513350724808`}, {4.628780111064041`, 1.0934563082740338`,
1.0933691855477623`}, {4.633090708056657`, 1.0979082616536864`,
1.0975419163852478`}, {4.633462986477512`, 1.104524343003987`,
1.091597284512775`}, {4.628903205161724`, 1.109486648788766`,
1.0774592939914904`}, {4.6330980858689195`, 1.0979635232925447`,
1.0974981913062274`}, {4.6204607209485875`, 1.108232773926825`,
1.0600789919540927`}, {4.62990425209302`, 1.094538807792192`,
1.0945352613293138`}, {4.630930702558078`, 1.0955817609067156`,
1.09554653364904`}, {4.629678666879561`, 1.09437091868271`,
1.094255057105462`}, {4.627969195184841`, 1.0926419971885992`,
1.0925649298605031`}, {4.633882911429514`, 1.1004706133906128`,
1.0961376872121722`}, {4.610136004816116`, 1.0758456151691589`,
1.0662408450336203`}, {1.7821782426455937`, 1.7821782401419397`,
1.7821782375015325`}, {4.6339246596020365`, 1.1025497494617507`,
1.0945596302801377`}, {4.631343908337303`, 1.09519015974554`,
1.0951863886076638`}, {4.63182102998238`, 1.09605706223029`,
1.0960440015739492`}, {4.629898252957912`, 1.0945692425507279`,
1.0944935207279352`}, {4.630253809169652`, 1.0957021864743024`,
1.0956692010308122`}, {4.634215841103628`, 1.0989181624347608`,
1.0987812653262299`}, {4.629254578264443`, 1.095839661013931`,
1.0919355531118964`}, {4.633899238572557`, 1.1024902979830358`,
1.094569063179371`}, {1.7821782156518977`, 1.7821782075738928`,
1.7821782069058023`}, {4.630998538365859`, 1.095634064809003`,
1.09563031143123`}, {4.631606559140232`, 1.0962631537168928`,
1.0962186968676015`}, {4.630883395500399`, 1.0956862064460648`,
1.0955470245026304`}, {4.631155056489257`, 1.0960407027128076`,
1.0959461846919822`}, {4.63464361875729`, 1.0995610241914973`,
1.0990454869857198`}, {4.627769338691886`, 1.0995350826784915`,
1.0991359329884394`}, {4.632311180052006`, 1.101956615177343`,
1.0919215762818375`}, {1.7821782187421231`, 1.7821782170363305`,
1.78217821679206`}, {4.636442936858322`, 1.1005782415087286`,
1.0952089619070715`}, {4.632912186334626`, 1.1076301678898268`,
1.0869886280431216`}, {1.7821782530421315`, 1.7821782134749404`,
1.782178138791525`}, {4.625809233693003`, 1.0904755549048777`,
1.0904102179403978`}, {4.631242478056988`, 1.0960148542230328`,
1.0957370954960894`}, {4.626743018852252`, 1.0914221728041034`,
1.0913318905153555`}, {4.629842318051541`, 1.0945367126492624`,
1.0944156018235482`}, {4.630628716997203`, 1.09532979288445`,
1.0951964332422914`}, {1.7821782560829351`, 1.782178182350041`,
1.7821781676419366`}, {1.7821782654476221`, 1.7821781824688236`,
1.7821781347476844`}, {4.632227349478559`, 1.104727515221102`,
1.0889620929179047`}, {4.629859641853101`, 1.096104769343091`,
1.0928795107662506`}, {4.633720612182211`, 1.0985241804219381`,
1.0980798262437301`}, {4.633902741071321`, 1.0987061392069732`,
1.0983676859125169`}, {4.628642585480639`, 1.0933049679935847`,
1.0932461715001067`}, {4.629793630644775`, 1.0944560311703375`,
1.094399533089984`}, {1.7821782224231548`, 1.7821782156826125`,
1.7821782099317534`}, {4.632930247698989`, 1.107013147881394`,
1.0878676666309512`}, {1.782178218917672`, 1.7821782183946724`,
1.7821782183835977`}, {4.632045129705727`, 1.097482137749623`,
1.0966870079349649`}, {4.633878820337265`, 1.1004114953497883`,
1.096609526352466`}, {4.625519131206819`, 1.0902808833820963`,
1.0900233521607257`}, {4.629601133885636`, 1.0942965094177077`,
1.0941734472750821`}, {4.631343837939016`, 1.0960086651853445`,
1.0959448480765503`}, {4.633480505178389`, 1.1027431385560358`,
1.0918619122451034`}, {4.626009473558213`, 1.1107657846739325`,
1.0699175324887884`}, {1.7821782297366828`, 1.7821782293999358`,
1.7821782285594006`}, {4.626738785159658`, 1.0914076418625709`,
1.0913352107350245`}, {4.633692345091232`, 1.0983942746671815`,
1.0982590222946043`}, {4.633769336942441`, 1.0978487487674213`,
1.097362331542783`}, {4.626099642203344`, 1.0907544195721688`,
1.0907134628460198`}, {4.629923721128267`, 1.0945852641261846`,
1.0945274534532443`}, {4.6347198659819`, 1.0997070919323404`,
1.0989992869491565`}, {4.625291636992392`, 1.0900774353944462`,
1.0897726915254806`}, {4.6315156780056`, 1.0970629406096133`,
1.0953368849516405`}, {4.63393630249651`, 1.1030166055290416`,
1.0941142774457744`}, {4.63356462183661`, 1.1002290366821137`,
1.0961640273187274`}, {4.6278333188763305`, 1.0926968521382137`,
1.0922383244557632`}, {4.627390863776004`, 1.0920729530001598`,
1.0919751701834868`}, {4.633744388618624`, 1.09868414666879`,
1.098283262089589`}, {4.633113791408536`, 1.0985553895663422`,
1.098517901800121`}, {4.634393384544145`, 1.0992233389163328`,
1.0988289785319716`}, {4.626591518815212`, 1.0913984682803213`,
1.091051233312806`}, {4.634180146226997`, 1.1009684460975018`,
1.0966554794753278`}, {1.782178244139888`, 1.7821782194218463`,
1.7821781683450015`}, {1.782178217928397`, 1.7821782178164949`,
1.7821782175000576`}, {4.634214196454377`, 1.1003124954298034`,
1.095828399123256`}, {4.633938768723598`, 1.1002042673506942`,
1.0968438145985924`}, {4.6291888256230225`, 1.093851808481601`,
1.0937913116526203`}, {4.633814282170795`, 1.098593651417665`,
1.0983003432314247`}, {4.630526286509474`, 1.0954116272523202`,
1.0949067524944915`}, {4.633667617106059`, 1.0993672981737561`,
1.0972356898762872`}, {4.633841894074934`, 1.1008356192420206`,
1.0961130726136301`}, {1.782178438465777`, 1.782178438383918`,
1.7821784383770773`}, {1.7821780107503244`, 1.7821780105545248`,
1.7821780105522056`}, {4.633230319153905`, 1.0989239680661282`,
1.0984223864423985`}, {4.630540874760529`, 1.095223567355211`,
1.0951243764170415`}, {4.628711693836818`, 1.0933712082945442`,
1.0933173825349958`}, {4.631566944510164`, 1.0964109775559194`,
1.095990753718179`}, {4.633846908941807`, 1.0992282182954605`,
1.0976293328271305`}, {4.629774744358188`, 1.094437376363828`,
1.094378224912907`}, {1.782178238439778`, 1.7821782209337977`,
1.7821781636560858`}, {1.7821782810378486`, 1.7821781758050574`,
1.7821781197013087`}, {4.6256304139952125`, 1.0937744666819305`,
1.0867486367338954`}, {4.631018050878536`, 1.095711314533029`,
1.0955902958199117`}, {4.6297032797206645`, 1.0943620634907198`,
1.094310127804341`}, {4.631705722167048`, 1.0964866194616316`,
1.0961907608446129`}, {4.631540577476475`, 1.0961813095383712`,
1.096166173824984`}, {4.634614969785078`, 1.099371310463111`,
1.0991271018393725`}, {4.620046941895322`, 1.1131725575125417`,
1.0489318767983717`}, {4.6273489000827865`, 1.0920106093376472`,
1.0919524059740469`}, {1.7821783723532392`, 1.7821783723388531`,
1.7821783722439877`}, {4.63132931318714`, 1.0960295964212226`,
1.0958951735122275`}, {4.630638591187705`, 1.0953009198223105`,
1.0952425202130687`}, {4.631671171622347`, 1.096406968994134`,
1.0962041388821235`}, {4.634041538666166`, 1.0989640632655948`,
1.0983852552672773`}, {4.626786879562127`, 1.0914572468808377`,
1.0913822274583929`}, {4.639019084772859`, 1.0990920887044595`,
1.0962219177868173`}, {4.622465386784579`, 1.1073275088598613`,
1.0667616173868322`}, {1.7821782956040764`, 1.7821781492337998`,
1.7821781289346912`}, {1.7821782594901547`, 1.78217821620207`,
1.7821781237820011`}, {4.6334146720795495`, 1.1023447888006563`,
1.0937431773535282`}, {1.7821782184827115`, 1.7821782181619652`,
1.782178217287757`}, {4.632808050980037`, 1.1005213586009075`,
1.0959778700660983`}, {4.631454765268613`, 1.0962256499135201`,
1.0961587107551167`}, {4.634462789037572`, 1.0996098967208796`,
1.0983714371360511`}, {4.634406522059262`, 1.099198209168747`,
1.0988833456817673`}, {4.634482926198381`, 1.0989966149307038`,
1.0983706429424749`}, {1.7821781653890925`, 1.7821781653158855`,
1.7821781651069306`}, {1.7821782210980923`, 1.7821782194464595`,
1.782178197079796`}, {4.630900131088422`, 1.1032755673082677`,
1.0877633982862662`}, {4.6179917850754775`, 1.0830208113740156`,
1.0806252779492975`}, {4.630553147001923`, 1.095239979484812`,
1.0951315938670876`}, {4.632924856347562`, 1.0977680845299425`,
1.0973499273990555`}, {4.627769516042762`, 1.092453300557214`,
1.0923539079547797`}, {4.62990784663922`, 1.094602066729353`,
1.0944817660301243`}, {4.619364588300723`, 1.0892668625348958`,
1.078714066451085`}, {4.624269130802406`, 1.0993246357282849`,
1.078424564871748`}, {1.782178218306192`, 1.782178215238749`,
1.7821782085563591`}, {4.633228883693543`, 1.1018536175202365`,
1.0938618200521015`}, {4.634088862668109`, 1.1007050305580237`,
1.0967359484029446`}, {4.63128952265368`, 1.0995497461917003`,
1.0990784492582182`}, {4.633797254993305`, 1.0986267156785452`,
1.0982854885910196`}, {4.6291490746184865`, 1.0938150054135`,
1.0937506020627934`}, {1.7821782598516867`, 1.7821781947568438`,
1.7821781520706579`}, {4.631522118244263`, 1.1051028005434806`,
1.0871177444140283`}, {4.6177146803702795`, 1.0977899029761218`,
1.0667855246505262`}, {1.782178254783224`, 1.7821781869388462`,
1.7821781663093057`}, {4.627434633070776`, 1.0922624319856795`,
1.0918743556468273`}, {4.632717140975467`, 1.098749248142308`,
1.0959527127877884`}, {4.62776684109561`, 1.0925350378877072`,
1.0922639652744062`}, {4.630495478936828`, 1.0952029445723555`,
1.0950544615128697`}, {4.633540237993966`, 1.0988163795669343`,
1.0959814596721034`}, {4.639794717089401`, 1.1001577133552358`,
1.0965335758137171`}, {4.618667129183747`, 1.0914697636148154`,
1.0626585163141091`}, {1.7821782177777197`, 1.7821782177530632`,
1.7821782177454037`}, {4.628485156819136`, 1.1034581077387204`,
1.0827271414714743`}, {1.7821782278802916`, 1.782178217488827`,
1.7821781921791753`}, {4.6328189459460845`, 1.0976302355123888`,
1.0972761501959412`}, {4.629891889529158`, 1.0945317705369217`,
1.094518878131033`}, {4.632949199013176`, 1.0978322044921611`,
1.0973349018150802`}, {4.634041131289353`, 1.0989149145226065`,
1.0986290192964505`}, {4.633758257256547`, 1.0996488670057383`,
1.096932551986466`}, {4.634269605539588`, 1.1032729059160655`,
1.0944730797786553`}, {4.6298148454716355`, 1.0946679565720523`,
1.0942297811291546`}, {4.634105299339605`, 1.0999309930998626`,
1.097547337197966`}, {4.632978164086134`, 1.0976135763452626`,
1.0976103876151617`}, {4.628352535998441`, 1.093008980537016`,
1.0929611774665182`}, {4.627543349800665`, 1.0923261253648884`,
1.0920291550289019`}, {4.631004400572808`, 1.097501383127232`,
1.0971314274238486`}, {4.627848667464798`, 1.0996417177879376`,
1.099051569643019`}, {4.632747178279302`, 1.0987487853356863`,
1.0960133177159899`}, {1.7821782772870258`, 1.7821781727302521`,
1.78217814603835`}, {1.7821782591781807`, 1.7821781986276788`,
1.7821781342985743`}, {1.7821782292513486`, 1.782178209960088`,
1.7821782005052107`}, {4.633379891862798`, 1.1002277159750984`,
1.0957452490694857`}, {4.634220601656808`, 1.1001596088651748`,
1.098351795735992`}, {4.6279972186905685`, 1.092679954655677`,
1.0925806233913598`}, {4.633904019599938`, 1.098789775183122`,
1.098287034301549`}, {4.635624513359043`, 1.0990051448475928`,
1.0983559171595014`}, {4.625680244024465`, 1.0904521517212464`,
1.090174269340893`}, {4.631431812899657`, 1.1048346229343478`,
1.0841400658582978`}, {1.78217821136866`, 1.782178210616978`,
1.7821782071885972`}, {4.632634854006185`, 1.1002144208164677`,
1.0959999807561733`}, {4.625870487461109`, 1.0906981831736537`,
1.090308541205196`}, {4.62984640924288`, 1.0945391685826418`,
1.0944191951011126`}, {4.628661797582045`, 1.0933419418133776`,
1.0932487064125536`}, {4.6339237755284985`, 1.0987715514896998`,
1.0983425793316204`}, {4.627162319798182`, 1.0931121331337892`,
1.0904793979731253`}, {4.629723376110292`, 1.0957553368218975`,
1.0929567758801673`}, {1.782178210899426`, 1.782178210753537`,
1.78217821072719`}, {4.632915375204023`, 1.1039125964643002`,
1.0919587571950926`}, {4.632916161496431`, 1.0980668745734246`,
1.0970342761187224`}, {4.630656692202246`, 1.0953573868124657`,
1.095221721006586`}, {4.6298684882261325`, 1.0945498638367779`,
1.094453221744989`}, {4.633420493902133`, 1.0987424198505593`,
1.098115857149877`}, {4.632647850247808`, 1.0977684134619097`,
1.0967942473217422`}, {4.628964891887905`, 1.0937916322005776`,
1.093406991615828`}, {4.633956766495952`, 1.098849483687892`,
1.098329810431893`}, {1.7821782657916128`, 1.782178182563235`,
1.7821781351169887`}, {4.631752709518959`, 1.0974384186951538`,
1.0953328414826287`}, {4.629100018056158`, 1.109735335556899`,
1.0776020488399833`}, {1.7821782406783102`, 1.7821782197467901`,
1.7821781576231295`}, {1.7821782142229652`, 1.7821782134084538`,
1.7821782131318817`}, {4.6347259226908095`, 1.099551036963113`,
1.0987973177176564`}};
``````

I wish to eliminate duplicates here, however I have difficulty of finding the proper criterion

after applying `DeleteDuplicates(Floor(list, 0.001))` I reduce the number of elements in the list to 91

``````{{1.782, 1.782, 1.782}, {4.632, 1.106, 1.087}, {4.627, 1.106,
1.077}, {4.631, 1.096, 1.096}, {4.632, 1.097, 1.096}, {4.627, 1.092,
1.092}, {4.629, 1.094, 1.094}, {4.63, 1.095, 1.095}, {4.634, 1.099,
1.098}, {4.634, 1.101, 1.096}, {4.633, 1.099, 1.097}, {4.631,
1.095, 1.095}, {4.632, 1.095, 1.095}, {4.632, 1.097, 1.097}, {4.628,
1.093, 1.093}, {4.629, 1.093, 1.093}, {4.631, 1.098,
1.094}, {4.634, 1.102, 1.094}, {4.63, 1.097, 1.093}, {4.633, 1.098,
1.098}, {4.626, 1.091, 1.091}, {4.633, 1.099, 1.095}, {4.634, 1.099,
1.099}, {4.631, 1.099, 1.096}, {4.633, 1.097, 1.097}, {4.61, 1.072,
1.065}, {4.619, 1.089, 1.077}, {4.633, 1.099, 1.094}, {4.634, 1.1,
1.097}, {4.63, 1.095, 1.094}, {4.63, 1.094, 1.094}, {4.633, 1.104,
1.091}, {4.628, 1.109, 1.077}, {4.62, 1.108, 1.06}, {4.633, 1.1,
1.096}, {4.61, 1.075, 1.066}, {4.633, 1.102, 1.094}, {4.634, 1.098,
1.098}, {4.629, 1.095, 1.091}, {4.631, 1.096, 1.095}, {4.627, 1.099,
1.099}, {4.632, 1.101, 1.091}, {4.636, 1.1, 1.095}, {4.632, 1.107,
1.086}, {4.625, 1.09, 1.09}, {4.632, 1.104, 1.088}, {4.629, 1.096,
1.092}, {4.632, 1.107, 1.087}, {4.633, 1.102, 1.091}, {4.626, 1.11,
1.069}, {4.626, 1.09, 1.09}, {4.625, 1.09, 1.089}, {4.631, 1.097,
1.095}, {4.633, 1.103, 1.094}, {4.627, 1.092, 1.091}, {4.634, 1.1,
1.096}, {4.634, 1.1, 1.095}, {4.625, 1.093, 1.086}, {4.62, 1.113,
1.048}, {4.639, 1.099, 1.096}, {4.622, 1.107, 1.066}, {4.633, 1.102,
1.093}, {4.632, 1.1, 1.095}, {4.63, 1.103, 1.087}, {4.617, 1.083,
1.08}, {4.619, 1.089, 1.078}, {4.624, 1.099, 1.078}, {4.633, 1.101,
1.093}, {4.631, 1.099, 1.099}, {4.631, 1.105, 1.087}, {4.617, 1.097,
1.066}, {4.632, 1.098, 1.095}, {4.633, 1.098, 1.095}, {4.639, 1.1,
1.096}, {4.618, 1.091, 1.062}, {4.628, 1.103, 1.082}, {4.633, 1.099,
1.096}, {4.634, 1.103, 1.094}, {4.634, 1.099, 1.097}, {4.628,
1.093, 1.092}, {4.631, 1.097, 1.097}, {4.632, 1.098, 1.096}, {4.633,
1.1, 1.095}, {4.634, 1.1, 1.098}, {4.635, 1.099, 1.098}, {4.631,
1.104, 1.084}, {4.627, 1.093, 1.09}, {4.629, 1.095, 1.092}, {4.632,
1.103, 1.091}, {4.632, 1.098, 1.097}, {4.629, 1.109, 1.077}}
``````

however, many of the elements in the list are still considered (by me) as duplicates, for example:

the elements `{4.631, 1.099, 1.099}, {4.632, 1.098, 1.097},{4.634, 1.1, 1.098}` are duplicates.
at total I expect the length of the list after removing all the duplicates to be no longer than 10.

What criterion should I apply to eliminate these duplicates? A metric distance for example can be useful, how can it be applied?