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==== Table 2. Benchmark results for cases with tetrahedral symmetry and its variations ====

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Case   t1   t2     <V_rms>        Nu_top        Nu_botm           <T>            T_mid_min        T_mid_max     Velo_mid_min    Velo_mid_max
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BM1A   0.7 1.0  32.67(0.00043) 3.5132(0.00018) 3.4920(3.2e-05) 0.2172(1.5e-05) 0.01750(5.3e-06) 0.8974(0.00015) -29.98(0.0051 ) 114.8(0.015 )
 SHH06          32.5894        3.4864          3.4864
 RSZ96          32.19          3.4423
 YK04           32.05          3.4430
BM1B   1.0 1.9  27.36(0.00013) 3.2701(0.00020) 3.2502(8.8e-05) 0.2362(1.5e-05) 0.02124(7.0e-05) 0.9085(0.00062) -17.21(0.0081 ) 139.8(0.16  )
 SHH06          27.2591        3.2398          3.2399
 RSZ96          26.80          3.2337
BM1C   0.6 0.9  25.85(0.0012 ) 3.1739(0.00021) 3.1554(4.7e-05) 0.2433(1.5e-05) 0.02320(2.5e-05) 0.9126(0.0013 ) -15.03(0.0042 ) 147.7(0.40  )
 SHH06          25.7300        3.1447          3.1450
 RSZ96          25.69          3.1615
 YK04           26.11          3.1330
BM1D   1.5 2.0  23.12(6.4e-05) 2.9365(5.3e-06) 2.9211(4.5e-06) 0.2654(1.4e-06) 0.03324(6.1e-06) 0.9234(0.00019) -10.75(0.0021 ) 170.0(0.11  )
BM1E   1.0 1.5  22.91(0.0034 ) 2.5472(0.00048) 2.5354(0.00039) 0.3125(1.2e-05) 0.06948(1.2e-05) 0.9459(0.00063) -6.970(0.13   ) 227.3(0.80  )
BM1F   2.6 3.6  29.24(0.077  ) 2.0421(0.0051 ) 2.0329(0.0062 ) 0.3512(0.0014 ) 0.15227(0.00033) 0.9606(0.0029 ) -21.04(1.6    ) 298.1(5.8   )
BM1G   1.2 1.7  50.21(0.0083 ) 2.7383(0.00055) 2.7431(7.7e-05) 0.5040(0.00010) 0.27008(0.00039) 0.9452(0.00093) -23.90(0.11   ) 300.2(6.3   )
BM1H   0.8 1.0  87.66(0.010  ) 3.0338(0.0021 ) 3.0681(0.0024 ) 0.5457(0.00011) 0.47030(0.00164) 0.9690(0.0014 ) -46.98(0.11   ) 806.9(18    )
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Note:
1) t1 and t2 are the starting and ending times for computing the averages, &lt;V_rms&gt;, Nu_top, Nu_botm, and &lt;T&gt; are averaged RMS 
   velocity, nussult number at the top and bottom boundaries, and temperature, respectively. T_mid_min, T_mid_max, velo_mid_min, and 
   velo_mid_max are the minimum and maximum temperatures, minimum and maximum velocities at the middle depth of the mantle.
2) The numbers in parentheses are standard deviations.
3) SHH06 is Stemmer et al. {2006}, RSZ96 is Ratcliff et al. {1996}, and YK04 is Yoshida and Kageyama {2004}. Resolution for these studies 
   is given in Table 1.  

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