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`, 
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    1.7821781281225377`}, {4.633878705367475`, 1.0987733497370047`, 
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    1.0975419163852478`}, {4.633462986477512`, 1.104524343003987`, 
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    1.0945352613293138`}, {4.630930702558078`, 1.0955817609067156`, 
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    1.0662408450336203`}, {1.7821782426455937`, 1.7821782401419397`, 
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    1.0904102179403978`}, {4.631242478056988`, 1.0960148542230328`, 
    1.0957370954960894`}, {4.626743018852252`, 1.0914221728041034`, 
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    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?