LeBron James has the most career points in the playoffs when grabbing 10+ rebounds and recording 10+ assists, with 7,631 points.

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most playoffs with 20 points 10 rebounds and 10 assists by a player
Interpreted as:
most playoffs with 20 or more points 10 or more rebounds and 10 or more assists by a player
JamesJordanAbdul-JabbarBryantO'NealDuncanMaloneWestDurantParkerWadeBirdHavlicekOlajuwonJohnsonNowitzkiPippenBaylorChamberlainHardenMcHalePierceJohnsonErvingGinobili7.6k6.0k5.8k5.6k5.3k5.2k4.8k4.5k4.5k4.0k4.0k3.9k3.8k3.8k3.7k3.7k3.6k3.6k3.6k3.2k3.2k3.2k3.1k3.1k3.1k
NAMEGPPTSREBASTMPGPPGRPGAPGSPGBPGTPGFGMFGAFG%3PM3PA3P%FTMFTAFT%MINSTLBLKTOVPF+/-
LeBron JamesLeBron James2667,6312,3911,91941.528.79.07.21.70.93.710.220.749.51.64.833.76.68.974.011,035454252975616+1310
Michael JordanMichael Jordan1795,9871,1521,02241.833.46.45.72.10.93.112.225.148.70.82.533.28.29.982.87,474376158546541+294
Kareem Abdul-JabbarKareem Abdul-Jabbar2375,7622,48176737.324.310.53.21.02.42.69.918.753.30.00.00.04.46.074.08,851189476447797
Kobe BryantKobe Bryant2205,6401,1191,04039.325.65.14.71.40.72.99.220.544.81.34.033.16.07.481.68,641310144647660+555
Shaquille O'NealShaquille O'Neal2165,2502,50858237.524.311.62.70.52.13.09.416.856.30.00.05.410.750.48,098117459649769+638
Tim DuncanTim Duncan2515,1722,85976437.320.611.43.00.72.32.57.915.750.10.00.114.34.87.068.99,370168568633701+1090
Karl MaloneKarl Malone1934,7612,06261041.024.710.73.21.30.72.89.019.546.30.00.216.26.68.973.67,907258135550662+123
Jerry WestJerry West1534,45785597041.329.15.66.30.00.010.622.646.97.99.880.56,32100451
Kevin DurantKevin Durant1514,4541,18261040.329.57.84.01.01.23.210.020.947.82.26.335.77.38.486.56,083157182480375+750
Tony ParkerTony Parker2264,0456661,14334.317.92.95.10.90.12.67.115.546.10.51.730.93.14.273.17,75819819594429+581
Dwyane WadeDwyane Wade1773,95492887037.822.35.24.91.51.03.38.217.347.40.61.733.85.46.978.06,697273175583467+432
Larry BirdLarry Bird1643,8971,6831,06242.023.810.36.51.80.93.18.918.847.20.51.532.15.56.289.06,886296145506466
John HavlicekJohn Havlicek1723,7761,18682539.922.06.94.81.10.38.419.443.65.16.183.66,8606016527
Hakeem OlajuwonHakeem Olajuwon1453,7551,62145839.625.911.23.21.73.32.910.419.652.80.00.122.25.17.171.95,749245472424562-29
Magic JohnsonMagic Johnson1903,7011,4652,34639.719.57.712.31.90.33.76.813.450.60.31.124.15.66.783.87,53835864696524
Dirk NowitzkiDirk Nowitzki1453,6631,44636040.725.310.02.51.00.92.38.418.246.21.02.836.57.48.389.25,895149129328407+48
Scottie PippenScottie Pippen2083,6421,5831,04839.017.57.65.01.90.92.96.414.544.41.03.230.33.75.172.48,105395185602686+232
Elgin BaylorElgin Baylor1343,6231,72454141.127.012.94.010.423.643.96.38.277.15,510435
Wilt ChamberlainWilt Chamberlain1603,6073,91367347.222.524.54.28.917.152.24.710.246.57,559412
James HardenJames Harden1373,19174781935.423.35.56.01.70.53.47.016.342.82.57.533.26.97.986.84,84423873470426+340
Kevin McHaleKevin McHale1693,1821,25327433.818.87.41.60.41.71.97.112.756.10.00.138.14.55.878.85,71665281326571
Paul PiercePaul Pierce1703,18098557936.618.75.83.41.20.62.86.014.242.31.64.635.55.16.183.06,229204105476547+160
Dennis JohnsonDennis Johnson1803,1167811,00638.917.34.35.61.40.62.76.514.843.90.20.823.64.25.280.26,994247113480575
Julius ErvingJulius Erving1413,08899459437.521.97.04.21.71.73.28.417.348.60.10.319.45.06.477.95,288235239396403
Manu GinobiliManu Ginobili2183,05487482727.914.04.03.81.30.32.24.410.143.31.54.235.83.84.681.76,07529261481588+951
StatMuse has season-level data for rebounds going back to the 1951 playoffs.