The International Celestial Reference Frame, now ICRF2, is a very impressive human achievement in science. (Or perhaps better described as impressive engineering because there is no hypothesis being tested.)
Although its usefulness technically has limited scope in space and time, that scope is huge: any point in space where you don't get parallax on distant galaxies, and any point in time where the distant galaxies haven't done much proper motion. I can think of no other human achievement which is so grand but limited in such a way.
I think merely the positions of quasars does not establish the 3 dimensional origin of the reference frame, e.g., the barycenter of the solar system, unless there is VLBI magic that I'm failing to understand. The positions of the quasars are going to appear to be the same when viewed from any point in the solar system. In order to establish an origin, I think one also needs a solar system model which can provide testable predictions of where planets and other bodies will appear in our sky (ephemerides) with celestial coordinates expressed relative to ICRF. Such a model would be a reverse orrery for specifying time.
Below are the 295 defining sources of ICRF2 reexpressed in decimal right ascension and declination. The original specification used a precision of 1 part in 36000*10^7 of an hour of right ascension, and 1 part in 3600*10^7 of a degree of declination. The decimal conversions below provide precision of 1 part in 10000*10^7 of an hour for RA and 1 part in 1000*10^7 of a degree of D, which is less precise. However, the smallest uncertainties in the source are 1 part in 132*10^7 of an hour of RA, and 1 part in 8.7*10^7 of a degree of D, which exceeds the precision. (Incidentally, the angular resolution of the Hubble Space Telescope is 0.05 arc second, compared to the largest uncertainty in the ICRF2 defining sources of 0.0003101 arc second of declination, so ICRF2 is at least 160 times more precise than Hubble.)
The coordinates define the vertices of a polyhedron inscribed within a sphere which, if manufactured, would be an elegant way to store the information, but I don't think any manufacturing process can be precise to such tolerances.
An astronomer starting anew, given just these coordinates, would do a VLBI survey of thousands of extragalactic radio sources and align his or her measurements with this set, seeking approximate matching subsets. I don't know how hard this computational geometry matching problem is, though I suspect it is easy.
RA Declination 0.07657097329 -47.6054454972 0.17527941718 10.9748623285 0.18367964957 -26.2092713936 0.22531394537 40.8603178067 0.26974682077 -0.2534570393 0.32938511650 73.4583381777 0.37567811365 6.1345191891 0.64023433120 41.6183334176 0.84481038543 -9.4847806302 0.85263939448 -42.4425814578 1.04604510624 58.4030935003 1.11252999125 -40.5722111748 1.15429866833 -60.8301277691 1.20161797709 22.7441073308 1.22416855651 49.8066786595 1.31590615741 -21.6917055552 1.36155417872 11.8306703059 1.55160071002 -52.0010960336 1.61627633496 47.8580833457 1.61909267492 31.3766264892 1.69050893207 -9.4787983859 1.91563607995 47.7240387703 2.05927360234 72.5482409149 2.08470148891 32.2083598483 2.29693187551 1.7471386307 2.40789672127 6.9898170943 2.49304072044 -78.7960004992 2.52941501509 13.3818656297 2.60865817238 -29.8987611878 2.61479048497 -61.6042176181 2.63122379926 28.8024972286 2.66263118549 -2.5780317783 3.05978950626 47.2711876224 3.06406426333 -62.1904305198 3.11184987443 62.7172289345 3.15100652782 10.4878724889 3.16558309832 -60.9775155973 3.18052220264 38.2482882978 3.21721170085 41.3336620996 3.42689287543 22.4001015520 3.57045958711 -40.1403882893 3.59831245601 -54.5069762980 3.75178237340 14.8970995006 3.81059571590 -27.8204348757 4.02921279794 21.1746075100 4.06493052732 -36.0838647524 4.09277871932 -13.1371363079 4.11639870433 -38.4411228769 4.27681790317 -18.8523166746 4.38772242438 -1.3425181676 4.41301168359 0.6017581577 4.49804465779 27.4105211928 4.56050829443 29.0987436207 4.65023740801 -45.3729341294 4.72545422293 34.6851844506 4.81879752802 11.3579434605 4.83484450037 -81.0172864786 4.95088311906 -23.4144500394 5.02022496768 -1.9872934037 5.02924189453 13.9353390049 5.11221909109 -61.1613871650 5.14510095889 84.5345955599 5.15762696351 10.1957222332 5.16732475828 18.0115504593 5.27914615776 -62.1181636677 5.30106236203 20.9145826361 5.37622929967 -61.1325370901 5.42538893059 -45.9651902399 5.43796425296 -48.5102198742 5.45908484666 3.5254212897 5.55440716185 48.3813354617 5.57660346934 -61.1019647391 5.60789788200 -34.0198523375 5.64732265339 -44.0858163657 5.66176833084 14.5626560276 5.66507818790 -28.6655410589 5.79281914475 27.3657896019 5.83599449527 -57.5401101473 5.92522378097 39.8136569351 5.99223142546 23.8983129912 6.05253618382 17.7046696001 6.77556277629 44.8546083677 6.80391568631 -30.7387943563 6.84016162645 -16.6277014421 6.98833223174 8.2252648062 7.00042376013 17.1560281917 7.17947357689 47.5364285324 7.36484679538 71.3434342848 7.42133548924 14.4204851917 7.43659312249 79.1919489468 7.50530902061 -11.6868334753 7.65500941581 1.6179494052 7.70076359625 49.0043358150 7.76502286698 -0.7382055152 7.77385393853 25.8172596543 7.81003035408 24.0066972310 7.84779048200 12.5180078268 8.04667554495 18.1636803877 8.08838321346 61.7399167491 8.13264960282 4.5429252784 8.14435174543 49.8434806676 8.14907001090 40.8791357949 8.19075203108 1.7811722949 8.25720690483 36.5875413588 8.30444433464 42.3792819206 8.43064954286 3.1568111314 8.51446838631 24.1832834453 8.61089312582 -20.2831955820 8.91357636862 20.1085113572 8.94494559670 -11.0873417195 9.24386484213 2.7664574831 9.37956062796 -39.9930745434 9.38734803640 38.8277528160 9.46439564332 -20.5808978897 9.87556282404 35.2145564053 9.97213101092 47.4188451207 9.97248600865 32.4006137598 9.97979030591 65.5652272385 10.10389147672 -50.3037418544 10.24640707127 23.0212696847 10.26753790769 5.2173170689 10.29052432699 61.2743046296 10.30305224746 35.7109557855 10.39542588888 -66.7801993757 10.41244710974 19.2056710069 10.55102996338 41.2683980327 10.55945119203 7.1905965843 10.61484433389 -37.7375182422 10.62113325966 -29.5674481485 10.69632823268 52.5578420324 10.73973959664 80.9109563966 10.74886423498 6.9272951820 10.80183905750 -19.1599240622 10.86355252081 21.3311982818 10.96987093878 81.2424097727 10.97489033541 1.5663399359 11.06450601992 -53.9501935081 11.07425387260 38.2088330734 11.23297085655 14.7074868324 11.43158664524 26.1722163011 11.45122012488 -18.9548449051 11.51480072554 38.2551519426 11.55557105325 0.6813436917 11.60682692581 -3.5081934637 11.76489560296 -69.9004993867 11.78286053230 39.9761956952 11.78371408383 -38.2030620611 11.79765389688 -7.4114280802 11.83867004835 24.2982875891 11.87144708760 -8.6842538562 11.98841818020 -66.5942853385 11.99217608604 29.2455074650 12.26298660031 -17.5292785973 12.29780054483 30.1168433108 12.37293045022 4.2210489388 12.39458159404 80.6678723442 12.47983991040 37.1033599620 12.65683009033 7.5047747968 12.71426918788 37.8500070124 12.76784225099 -7.5129373742 12.77966723192 -25.7970246639 12.91062655878 11.6849708833 12.91664484686 -71.6384546305 13.04790702102 57.8104470328 13.18316742482 32.5595693426 13.26888498332 -33.6497701405 13.45023925382 22.1806008258 13.48365136911 -56.1340738174 13.62771743824 -12.9568592394 13.72943321426 66.0404847503 13.73574435191 66.1032344124 13.88237081748 -44.2112187563 13.90191536726 -2.1008862346 13.95312360549 -15.4579963120 13.96538098096 76.7225141809 14.14902255566 -7.8740740056 14.32961038948 54.3874408854 14.32961493353 38.3634653035 14.41543260990 -68.1328040335 14.43028278231 14.4158060844 14.46563821260 -42.1053993331 14.57772037646 19.8668710615 14.76482674623 -16.4837830316 14.87768868053 -65.0342870442 14.90914232200 -40.2090317326 14.98315450334 4.2705057228 15.01351506164 47.8543161622 15.07360549484 10.4942218375 15.08513254421 3.4418924060 15.10264721327 37.5142034734 15.16747843462 57.0453821964 15.21403692359 -9.0999526633 15.22913705942 -10.2000734703 15.28244337873 19.5369422272 15.36378163329 43.6109078212 15.37713221909 -27.5029959493 15.82484356750 2.6169898388 15.84313034489 5.4529023406 15.96428721424 -0.0306704743 15.98063454539 -64.5415659464 15.99193683762 3.0800713564 16.12632287356 -33.5191425865 16.14616755154 10.4854932861 16.27517821106 -71.1420707062 16.27709911528 4.9924268749 16.32078461405 22.7966252996 16.40512139048 -68.1534712587 16.42969212225 -25.4606463330 16.48185828432 -61.8767771906 16.63707119363 57.3399941869 16.67489799217 39.7794523620 16.69034099028 22.9511202114 16.70218014041 68.9443768048 16.71592934811 -81.1430750469 17.01476501702 -26.1810348183 17.02912725384 -56.3655283203 17.06015034601 -62.2111133807 17.12622646417 1.8126942455 17.15954038702 -17.4814902701 17.32029124489 17.7517881392 17.45768077908 45.5110364846 17.55075160688 -13.0804300412 17.56130563283 -79.5988101926 17.57238292684 38.9642897429 17.65760847014 49.9176023447 17.66586918711 47.6328782102 17.73301559277 -3.8346157347 17.75978004745 17.3337288022 17.77056503811 62.4485384418 17.85911627033 9.6502023564 17.89513156786 28.8013719123 17.94808392673 15.5891184813 18.00687926701 38.8085270925 18.01268997678 78.4677829028 18.02564300586 44.0727500894 18.05652685194 -65.1268781137 18.16607548617 -45.8780594221 18.32927764403 -55.3557626051 18.39245941751 68.9646146089 18.40196343825 56.8504141214 18.48677843700 -58.2319893583 18.62464303833 -71.1454318303 18.70934491365 68.1570077178 18.80613571704 32.3173899286 18.82113119161 67.0949111938 19.18601469222 -20.1153080525 19.39227494852 -21.0759258485 19.41418220976 -29.2417002923 19.50171113735 -60.9358844866 19.52358799568 22.7253496169 19.62117148657 -39.9670980530 19.65740492986 -15.4286273384 19.67375783362 -69.1324920818 19.92853840788 51.5301517003 19.96661646519 -38.7517654885 20.01585845690 -17.8160201511 20.03622729324 47.4246593673 20.09863080562 -37.3948549593 20.18769748127 -15.7778482403 20.53194285309 12.3281500869 20.93787772743 -47.2465632350 21.02745393450 3.6920335994 21.14473115322 14.5075034216 21.15921905332 -41.1723903664 21.25817040432 29.5606574905 21.44186229579 -46.0966366731 21.48671552716 -15.6447336971 21.56953044345 -1.8881218864 21.65036368594 14.3933311693 21.78686961782 -75.6036735605 21.87356094431 17.5771652940 22.12881480670 -53.7760610341 22.20165730872 23.9279288409 22.38498071615 -34.9297715078 22.42979424806 -4.9503863217 22.49446787223 -8.5484542763 22.51013047359 69.7744658043 22.58701016031 -48.5996651391 22.65335442324 -57.0168998324 22.78442147857 -36.9628622118 22.81074603825 -32.5978299872 22.88538032594 19.7096190964 22.95480642291 7.7200840214 22.96832302356 -27.9725713174 23.06210128348 -68.1270674918 23.34579349942 5.2305423769 23.48825120841 -47.5053096779 23.60944030460 -41.2561066466 23.78885113739 -51.1766848564 23.90838755212 -15.2197813946 23.93352261274 -68.3342976968 23.96479613558 -53.1871359323 23.96968955767 -10.3357253670 23.99255022150 38.8450884151 23.99319209526 -31.5621734031
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