From 3cb30e2a6ba8c3cf04d01a4b02e73daef3f2464b Mon Sep 17 00:00:00 2001 From: Martin Kronbichler Date: Thu, 2 Apr 2020 14:20:44 +0200 Subject: [PATCH] Improve mesh quality of quarter hyper ball --- source/grid/grid_generator.cc | 42 +- tests/grid/grid_generator_01.output | 36 +- tests/grid/grid_generator_01b.output | 9020 +++++++++++++------------- 3 files changed, 4552 insertions(+), 4546 deletions(-) diff --git a/source/grid/grid_generator.cc b/source/grid/grid_generator.cc index 67d47f7d85..e6d950b543 100644 --- a/source/grid/grid_generator.cc +++ b/source/grid/grid_generator.cc @@ -4409,15 +4409,14 @@ namespace GridGenerator { const unsigned int dim = 2; - // equilibrate cell sizes at - // transition from the inner part - // to the radial cells + // the numbers 0.55647 and 0.42883 have been found by a search for the + // best aspect ratio (defined as the maximal between the minimal singular + // value of the Jacobian) const Point vertices[7] = {p + Point(0, 0) * radius, p + Point(+1, 0) * radius, - p + Point(+1, 0) * (radius / 2), - p + Point(0, +1) * (radius / 2), - p + Point(+1, +1) * - (radius / (2 * std::sqrt(2.0))), + p + Point(+1, 0) * (radius * 0.55647), + p + Point(0, +1) * (radius * 0.55647), + p + Point(+1, +1) * (radius * 0.42883), p + Point(0, +1) * radius, p + Point(+1, +1) * (radius / std::sqrt(2.0))}; @@ -5138,22 +5137,28 @@ namespace GridGenerator { const unsigned int dim = 3; - // equilibrate cell sizes at - // transition from the inner part - // to the radial cells + // the parameters a (intersection on the octant lines from center), b + // (intersection within the octant faces) and c (position inside the + // octant) have been derived by equilibrating the minimal singular value + // of the Jacobian of the four cells around the center point c and, as a + // secondary measure, to minimize the aspect ratios defined as the maximal + // divided by the minimal singular values throughout cells + const double a = 0.528; + const double b = 0.4533; + const double c = 0.3752; const Point vertices[15] = { center + Point(0, 0, 0) * radius, center + Point(+1, 0, 0) * radius, - center + Point(+1, 0, 0) * (radius / 2.), - center + Point(0, +1, 0) * (radius / 2.), - center + Point(+1, +1, 0) * (radius / (2 * std::sqrt(2.0))), + center + Point(+1, 0, 0) * (radius * a), + center + Point(0, +1, 0) * (radius * a), + center + Point(+1, +1, 0) * (radius * b), center + Point(0, +1, 0) * radius, - center + Point(+1, +1, 0) * (radius / std::sqrt(2.0)), - center + Point(0, 0, 1) * radius / 2., + center + Point(+1, +1, 0) * radius / std::sqrt(2.0), + center + Point(0, 0, 1) * radius * a, center + Point(+1, 0, 1) * radius / std::sqrt(2.0), - center + Point(+1, 0, 1) * (radius / (2 * std::sqrt(2.0))), - center + Point(0, +1, 1) * (radius / (2 * std::sqrt(2.0))), - center + Point(+1, +1, 1) * (radius / (2 * std::sqrt(3.0))), + center + Point(+1, 0, 1) * (radius * b), + center + Point(0, +1, 1) * (radius * b), + center + Point(+1, +1, 1) * (radius * c), center + Point(0, +1, 1) * radius / std::sqrt(2.0), center + Point(+1, +1, 1) * (radius / (std::sqrt(3.0))), center + Point(0, 0, 1) * radius}; @@ -5221,6 +5226,7 @@ namespace GridGenerator } + // Implementation for 3D only template <> void half_hyper_ball(Triangulation<3> &tria, diff --git a/tests/grid/grid_generator_01.output b/tests/grid/grid_generator_01.output index e0a2d90899..9779f2f56f 100644 --- a/tests/grid/grid_generator_01.output +++ b/tests/grid/grid_generator_01.output @@ -2585,37 +2585,37 @@ Single 0 147 #00ffff 2 3 0 1 0 32 900 0 25 0.0 0 0 -1 0 0 5 2400 1200 - 4200 1200 - 3672 -72 - 2400 -600 + 4403 1200 + 3943 -343 + 2400 -803 2400 1200 2 1 0 3 2 -1 800 0 -1 0.0 0 0 -1 0 0 2 2400 1200 - 4200 1200 + 4403 1200 2 1 0 3 2 -1 800 0 -1 0.0 0 0 -1 0 0 2 2400 1200 - 2400 -600 + 2400 -803 2 3 0 1 0 32 900 0 25 0.0 0 0 -1 0 0 5 6000 1200 4945 -1345 - 3672 -72 - 4200 1200 + 3943 -343 + 4403 1200 6000 1200 2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 6000 1200 4945 -1345 2 1 0 3 2 -1 800 0 -1 0.0 0 0 -1 0 0 2 6000 1200 - 4200 1200 + 4403 1200 2 3 0 1 0 32 900 0 25 0.0 0 0 -1 0 0 5 2400 -2400 - 2400 -600 - 3672 -72 + 2400 -803 + 3943 -343 4945 -1345 2400 -2400 2 1 0 3 2 -1 800 0 -1 0.0 0 0 -1 0 0 2 2400 -2400 - 2400 -600 + 2400 -803 2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 2400 -2400 4945 -1345 @@ -4359,16 +4359,16 @@ DEAL:3d::quarter_hyper_ball object "vertices" class array type float rank 1 shape 3 items 15 data follows 2.00000 -1.00000 0.00000 5.00000 -1.00000 0.00000 - 3.50000 -1.00000 0.00000 - 2.00000 0.500000 0.00000 - 3.06066 0.0606602 0.00000 + 3.58400 -1.00000 0.00000 + 2.00000 0.584000 0.00000 + 3.35990 0.359900 0.00000 2.00000 2.00000 0.00000 4.12132 1.12132 0.00000 - 2.00000 -1.00000 1.50000 + 2.00000 -1.00000 1.58400 4.12132 -1.00000 2.12132 - 3.06066 -1.00000 1.06066 - 2.00000 0.0606602 1.06066 - 2.86603 -0.133975 0.866025 + 3.35990 -1.00000 1.35990 + 2.00000 0.359900 1.35990 + 3.12560 0.125600 1.12560 2.00000 1.12132 2.12132 3.73205 0.732051 1.73205 2.00000 -1.00000 3.00000 diff --git a/tests/grid/grid_generator_01b.output b/tests/grid/grid_generator_01b.output index 977a9a8775..e79af72429 100644 --- a/tests/grid/grid_generator_01b.output +++ b/tests/grid/grid_generator_01b.output @@ -1,1877 +1,1877 @@ DEAL:2d::quarter_hyper_ball 2.00000 0.00000 2 0 -2.37500 0.00000 2 0 -2.34754 0.347541 2 0 -2.00000 0.375000 2 0 +2.41735 0.00000 2 0 +2.39342 0.393420 2 0 +2.00000 0.417353 2 0 2.00000 0.00000 2 0 -2.37500 0.00000 2 0 -2.75000 0.00000 2 0 -2.69508 0.320083 2 0 -2.34754 0.347541 2 0 -2.37500 0.00000 2 0 +2.41735 0.00000 2 0 +2.83471 0.00000 2 0 +2.78684 0.369487 2 0 +2.39342 0.393420 2 0 +2.41735 0.00000 2 0 -2.00000 0.375000 2 0 -2.34754 0.347541 2 0 -2.32008 0.695083 2 0 -2.00000 0.750000 2 0 -2.00000 0.375000 2 0 +2.00000 0.417353 2 0 +2.39342 0.393420 2 0 +2.36949 0.786840 2 0 +2.00000 0.834705 2 0 +2.00000 0.417353 2 0 -2.34754 0.347541 2 0 -2.69508 0.320083 2 0 -2.64017 0.640165 2 0 -2.32008 0.695083 2 0 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4.49441 1.66671 0.00000 2 0 @@ -2071,23 +2071,23 @@ DEAL:3d::quarter_hyper_ball 4.71937 1.13894 0.554830 2 0 4.77164 1.14805 0.00000 2 0 -4.39881 0.993620 0.00000 2 0 -4.15145 1.44090 0.00000 2 0 -4.09602 1.41280 0.440287 2 0 -4.32807 0.975788 0.473937 2 0 -4.39881 0.993620 0.00000 2 0 +4.44672 1.03103 0.00000 2 0 +4.21281 1.49701 0.00000 2 0 +4.15888 1.46705 0.457130 2 0 +4.38146 1.01195 0.491400 2 0 +4.44672 1.03103 0.00000 2 0 4.77164 1.14805 0.00000 2 0 -4.39881 0.993620 0.00000 2 0 +4.44672 1.03103 0.00000 2 0 4.49441 1.66671 0.00000 2 0 -4.15145 1.44090 0.00000 2 0 +4.21281 1.49701 0.00000 2 0 4.45278 1.64842 0.516335 2 0 -4.09602 1.41280 0.440287 2 0 +4.15888 1.46705 0.457130 2 0 4.71937 1.13894 0.554830 2 0 -4.32807 0.975788 0.473937 2 0 +4.38146 1.01195 0.491400 2 0 4.49441 1.66671 0.00000 2 0 4.12132 2.12132 0.00000 2 0 @@ -2095,71 +2095,71 @@ DEAL:3d::quarter_hyper_ball 4.45278 1.64842 0.516335 2 0 4.49441 1.66671 0.00000 2 0 -4.15145 1.44090 0.00000 2 0 -3.85616 1.85616 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0 -3.59099 1.59099 0.00000 2 0 -3.54175 1.54175 0.335432 2 0 -3.73925 1.17719 0.364239 2 0 -3.80849 1.21509 0.00000 2 0 +3.93120 1.32731 0.00000 2 0 +3.74061 1.74061 0.00000 2 0 +3.68641 1.68641 0.367879 2 0 +3.86498 1.28569 0.397925 2 0 +3.93120 1.32731 0.00000 2 0 -4.15145 1.44090 0.00000 2 0 -3.80849 1.21509 0.00000 2 0 +4.21281 1.49701 0.00000 2 0 +3.93120 1.32731 0.00000 2 0 -3.85616 1.85616 0.00000 2 0 -3.59099 1.59099 0.00000 2 0 +3.93097 1.93097 0.00000 2 0 +3.74061 1.74061 0.00000 2 0 -3.81900 1.81900 0.397611 2 0 -3.54175 1.54175 0.335432 2 0 +3.89133 1.89133 0.413835 2 0 +3.68641 1.68641 0.367879 2 0 -4.09602 1.41280 0.440287 2 0 -3.73925 1.17719 0.364239 2 0 +4.15888 1.46705 0.457130 2 0 +3.86498 1.28569 0.397925 2 0 4.71937 1.13894 0.554830 2 0 4.45278 1.64842 0.516335 2 0 @@ -2167,23 +2167,23 @@ DEAL:3d::quarter_hyper_ball 4.57324 1.09051 1.09051 2 0 4.71937 1.13894 0.554830 2 0 -4.32807 0.975788 0.473937 2 0 -4.09602 1.41280 0.440287 2 0 -4.00345 1.36104 0.872621 2 0 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1.09051 1.09051 2 0 @@ -2671,71 +2671,71 @@ DEAL:3d::quarter_hyper_ball 4.45278 0.516335 1.64842 2 0 4.71937 0.554830 1.13894 2 0 -4.32807 0.473937 0.975788 2 0 -4.21039 0.938299 0.938299 2 0 -4.00345 0.872621 1.36104 2 0 -4.09602 0.440287 1.41280 2 0 -4.32807 0.473937 0.975788 2 0 +4.38146 0.491400 1.01195 2 0 +4.26927 0.973225 0.973225 2 0 +4.06781 0.906307 1.41343 2 0 +4.15888 0.457130 1.46705 2 0 +4.38146 0.491400 1.01195 2 0 4.71937 0.554830 1.13894 2 0 -4.32807 0.473937 0.975788 2 0 +4.38146 0.491400 1.01195 2 0 4.57324 1.09051 1.09051 2 0 -4.21039 0.938299 0.938299 2 0 +4.26927 0.973225 0.973225 2 0 4.33687 1.01676 1.58279 2 0 -4.00345 0.872621 1.36104 2 0 +4.06781 0.906307 1.41343 2 0 4.45278 0.516335 1.64842 2 0 -4.09602 0.440287 1.41280 2 0 +4.15888 0.457130 1.46705 2 0 -4.39881 0.00000 0.993620 2 0 -4.32807 0.473937 0.975788 2 0 -4.09602 0.440287 1.41280 2 0 -4.15145 0.00000 1.44090 2 0 -4.39881 0.00000 0.993620 2 0 +4.44672 0.00000 1.03103 2 0 +4.38146 0.491400 1.01195 2 0 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4.45278 0.516335 1.64842 2 0 @@ -2743,23 +2743,23 @@ DEAL:3d::quarter_hyper_ball 4.12132 0.00000 2.12132 2 0 4.49441 0.00000 1.66671 2 0 -4.15145 0.00000 1.44090 2 0 -4.09602 0.440287 1.41280 2 0 -3.81900 0.397611 1.81900 2 0 -3.85616 0.00000 1.85616 2 0 -4.15145 0.00000 1.44090 2 0 +4.21281 0.00000 1.49701 2 0 +4.15888 0.457130 1.46705 2 0 +3.89133 0.413835 1.89133 2 0 +3.93097 0.00000 1.93097 2 0 +4.21281 0.00000 1.49701 2 0 4.49441 0.00000 1.66671 2 0 -4.15145 0.00000 1.44090 2 0 +4.21281 0.00000 1.49701 2 0 4.45278 0.516335 1.64842 2 0 -4.09602 0.440287 1.41280 2 0 +4.15888 0.457130 1.46705 2 0 4.09626 0.459790 2.09626 2 0 -3.81900 0.397611 1.81900 2 0 +3.89133 0.413835 1.89133 2 0 4.12132 0.00000 2.12132 2 0 -3.85616 0.00000 1.85616 2 0 +3.93097 0.00000 1.93097 2 0 4.45278 0.516335 1.64842 2 0 4.33687 1.01676 1.58279 2 0 @@ -2767,71 +2767,71 @@ DEAL:3d::quarter_hyper_ball 4.09626 0.459790 2.09626 2 0 4.45278 0.516335 1.64842 2 0 -4.09602 0.440287 1.41280 2 0 -4.00345 0.872621 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2 0 -4.00345 0.872621 1.36104 2 0 -4.21039 0.938299 0.938299 2 0 +4.26927 0.973225 0.973225 2 0 +4.06781 1.41343 0.906307 2 0 +3.90702 1.32153 1.32153 2 0 +4.06781 0.906307 1.41343 2 0 +4.26927 0.973225 0.973225 2 0 4.57324 1.09051 1.09051 2 0 -4.21039 0.938299 0.938299 2 0 +4.26927 0.973225 0.973225 2 0 4.33687 1.58279 1.01676 2 0 -4.00345 1.36104 0.872621 2 0 +4.06781 1.41343 0.906307 2 0 4.14940 1.47988 1.47988 2 0 -3.84115 1.27100 1.27100 2 0 +3.90702 1.32153 1.32153 2 0 4.33687 1.01676 1.58279 2 0 -4.00345 0.872621 1.36104 2 0 +4.06781 0.906307 1.41343 2 0 4.33687 1.58279 1.01676 2 0 4.02166 2.02166 0.908716 2 0 @@ -2863,71 +2863,71 @@ DEAL:3d::quarter_hyper_ball 4.14940 1.47988 1.47988 2 0 4.33687 1.58279 1.01676 2 0 -4.00345 1.36104 0.872621 2 0 -3.75708 1.75708 0.789790 2 0 -3.64753 1.64753 1.16056 2 0 -3.84115 1.27100 1.27100 2 0 -4.00345 1.36104 0.872621 2 0 +4.06781 1.41343 0.906307 2 0 +3.82693 1.82693 0.822237 2 0 +3.71491 1.71491 1.20923 2 0 +3.90702 1.32153 1.32153 2 0 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1.01676 1.58279 2 0 -4.00345 0.872621 1.36104 2 0 +4.06781 0.906307 1.41343 2 0 4.14940 1.47988 1.47988 2 0 -3.84115 1.27100 1.27100 2 0 +3.90702 1.32153 1.32153 2 0 3.89930 1.33617 1.89930 2 0 -3.64753 1.16056 1.64753 2 0 +3.71491 1.20923 1.71491 2 0 4.02166 0.908716 2.02166 2 0 -3.75708 0.789790 1.75708 2 0 +3.82693 0.822237 1.82693 2 0 4.14940 1.47988 1.47988 2 0 3.89930 1.89930 1.33617 2 0 @@ -2959,2873 +2959,2873 @@ DEAL:3d::quarter_hyper_ball 3.89930 1.33617 1.89930 2 0 4.14940 1.47988 1.47988 2 0 -3.84115 1.27100 1.27100 2 0 -3.64753 1.64753 1.16056 2 0 -3.51554 1.51554 1.51554 2 0 -3.64753 1.16056 1.64753 2 0 -3.84115 1.27100 1.27100 2 0 +3.90702 1.32153 1.32153 2 0 +3.71491 1.71491 1.20923 2 0 +3.58044 1.58044 1.58044 2 0 +3.71491 1.20923 1.71491 2 0 +3.90702 1.32153 1.32153 2 0 4.14940 1.47988 1.47988 2 0 -3.84115 1.27100 1.27100 2 0 +3.90702 1.32153 1.32153 2 0 3.89930 1.89930 1.33617 2 0 -3.64753 1.64753 1.16056 2 0 +3.71491 1.71491 1.20923 2 0 3.73205 1.73205 1.73205 2 0 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2.50533 2 0 +2.49140 1.01195 2.38146 2 0 -2.97579 0.473937 2.32807 2 0 -2.93830 0.938299 2.21039 2 0 +3.01195 0.491400 2.38146 2 0 +2.97323 0.973225 2.26927 2 0 3.13894 0.554830 2.71937 2 0 3.09051 1.09051 2.57324 2 0 @@ -5905,119 +5905,119 @@ DEAL:3d::quarter_hyper_ball 2.58064 0.580636 2.88543 2 0 2.55483 1.13894 2.71937 2 0 -2.83919 0.00000 2.02598 2 0 -3.21509 0.00000 1.80849 2 0 -3.44090 0.00000 2.15145 2 0 -2.99362 0.00000 2.39881 2 0 -2.83919 0.00000 2.02598 2 0 +2.91400 0.00000 2.12179 2 0 +3.32731 0.00000 1.93120 2 0 +3.49701 0.00000 2.21281 2 0 +3.03103 0.00000 2.44672 2 0 +2.91400 0.00000 2.12179 2 0 -2.81264 0.393045 1.93676 2 0 -3.17719 0.364239 1.73925 2 0 -3.41280 0.440287 2.09602 2 0 -2.97579 0.473937 2.32807 2 0 -2.81264 0.393045 1.93676 2 0 +2.88497 0.427971 2.04355 2 0 +3.28569 0.397925 1.86498 2 0 +3.46705 0.457130 2.15888 2 0 +3.01195 0.491400 2.38146 2 0 +2.88497 0.427971 2.04355 2 0 -2.83919 0.00000 2.02598 2 0 -2.81264 0.393045 1.93676 2 0 +2.91400 0.00000 2.12179 2 0 +2.88497 0.427971 2.04355 2 0 -3.21509 0.00000 1.80849 2 0 -3.17719 0.364239 1.73925 2 0 +3.32731 0.00000 1.93120 2 0 +3.28569 0.397925 1.86498 2 0 -3.44090 0.00000 2.15145 2 0 -3.41280 0.440287 2.09602 2 0 +3.49701 0.00000 2.21281 2 0 +3.46705 0.457130 2.15888 2 0 -2.99362 0.00000 2.39881 2 0 -2.97579 0.473937 2.32807 2 0 +3.03103 0.00000 2.44672 2 0 +3.01195 0.491400 2.38146 2 0 -3.21509 0.00000 1.80849 2 0 -3.59099 0.00000 1.59099 2 0 -3.85616 0.00000 1.85616 2 0 -3.44090 0.00000 2.15145 2 0 -3.21509 0.00000 1.80849 2 0 +3.32731 0.00000 1.93120 2 0 +3.74061 0.00000 1.74061 2 0 +3.93097 0.00000 1.93097 2 0 +3.49701 0.00000 2.21281 2 0 +3.32731 0.00000 1.93120 2 0 -3.17719 0.364239 1.73925 2 0 -3.54175 0.335432 1.54175 2 0 -3.81900 0.397611 1.81900 2 0 -3.41280 0.440287 2.09602 2 0 -3.17719 0.364239 1.73925 2 0 +3.28569 0.397925 1.86498 2 0 +3.68641 0.367879 1.68641 2 0 +3.89133 0.413835 1.89133 2 0 +3.46705 0.457130 2.15888 2 0 +3.28569 0.397925 1.86498 2 0 -3.21509 0.00000 1.80849 2 0 -3.17719 0.364239 1.73925 2 0 +3.32731 0.00000 1.93120 2 0 +3.28569 0.397925 1.86498 2 0 -3.59099 0.00000 1.59099 2 0 -3.54175 0.335432 1.54175 2 0 +3.74061 0.00000 1.74061 2 0 +3.68641 0.367879 1.68641 2 0 -3.85616 0.00000 1.85616 2 0 -3.81900 0.397611 1.81900 2 0 +3.93097 0.00000 1.93097 2 0 +3.89133 0.413835 1.89133 2 0 -3.44090 0.00000 2.15145 2 0 -3.41280 0.440287 2.09602 2 0 +3.49701 0.00000 2.21281 2 0 +3.46705 0.457130 2.15888 2 0 -2.81264 0.393045 1.93676 2 0 -3.17719 0.364239 1.73925 2 0 -3.41280 0.440287 2.09602 2 0 -2.97579 0.473937 2.32807 2 0 -2.81264 0.393045 1.93676 2 0 +2.88497 0.427971 2.04355 2 0 +3.28569 0.397925 1.86498 2 0 +3.46705 0.457130 2.15888 2 0 +3.01195 0.491400 2.38146 2 0 +2.88497 0.427971 2.04355 2 0 -2.78609 0.786090 1.84754 2 0 -3.13930 0.728477 1.67002 2 0 -3.36104 0.872621 2.00345 2 0 -2.93830 0.938299 2.21039 2 0 -2.78609 0.786090 1.84754 2 0 +2.85594 0.855942 1.96530 2 0 +3.24407 0.795850 1.79875 2 0 +3.41343 0.906307 2.06781 2 0 +2.97323 0.973225 2.26927 2 0 +2.85594 0.855942 1.96530 2 0 -2.81264 0.393045 1.93676 2 0 -2.78609 0.786090 1.84754 2 0 +2.88497 0.427971 2.04355 2 0 +2.85594 0.855942 1.96530 2 0 -3.17719 0.364239 1.73925 2 0 -3.13930 0.728477 1.67002 2 0 +3.28569 0.397925 1.86498 2 0 +3.24407 0.795850 1.79875 2 0 -3.41280 0.440287 2.09602 2 0 -3.36104 0.872621 2.00345 2 0 +3.46705 0.457130 2.15888 2 0 +3.41343 0.906307 2.06781 2 0 -2.97579 0.473937 2.32807 2 0 -2.93830 0.938299 2.21039 2 0 +3.01195 0.491400 2.38146 2 0 +2.97323 0.973225 2.26927 2 0 -3.17719 0.364239 1.73925 2 0 -3.54175 0.335432 1.54175 2 0 -3.81900 0.397611 1.81900 2 0 -3.41280 0.440287 2.09602 2 0 -3.17719 0.364239 1.73925 2 0 +3.28569 0.397925 1.86498 2 0 +3.68641 0.367879 1.68641 2 0 +3.89133 0.413835 1.89133 2 0 +3.46705 0.457130 2.15888 2 0 +3.28569 0.397925 1.86498 2 0 -3.13930 0.728477 1.67002 2 0 -3.49250 0.670865 1.49250 2 0 -3.75708 0.789790 1.75708 2 0 -3.36104 0.872621 2.00345 2 0 -3.13930 0.728477 1.67002 2 0 +3.24407 0.795850 1.79875 2 0 +3.63221 0.735758 1.63221 2 0 +3.82693 0.822237 1.82693 2 0 +3.41343 0.906307 2.06781 2 0 +3.24407 0.795850 1.79875 2 0 -3.17719 0.364239 1.73925 2 0 -3.13930 0.728477 1.67002 2 0 +3.28569 0.397925 1.86498 2 0 +3.24407 0.795850 1.79875 2 0 -3.54175 0.335432 1.54175 2 0 -3.49250 0.670865 1.49250 2 0 +3.68641 0.367879 1.68641 2 0 +3.63221 0.735758 1.63221 2 0 -3.81900 0.397611 1.81900 2 0 -3.75708 0.789790 1.75708 2 0 +3.89133 0.413835 1.89133 2 0 +3.82693 0.822237 1.82693 2 0 -3.41280 0.440287 2.09602 2 0 -3.36104 0.872621 2.00345 2 0 +3.46705 0.457130 2.15888 2 0 +3.41343 0.906307 2.06781 2 0 -2.99362 0.00000 2.39881 2 0 -3.44090 0.00000 2.15145 2 0 +3.03103 0.00000 2.44672 2 0 +3.49701 0.00000 2.21281 2 0 3.66671 0.00000 2.49441 2 0 3.14805 0.00000 2.77164 2 0 -2.99362 0.00000 2.39881 2 0 +3.03103 0.00000 2.44672 2 0 -2.97579 0.473937 2.32807 2 0 -3.41280 0.440287 2.09602 2 0 +3.01195 0.491400 2.38146 2 0 +3.46705 0.457130 2.15888 2 0 3.64842 0.516335 2.45278 2 0 3.13894 0.554830 2.71937 2 0 -2.97579 0.473937 2.32807 2 0 +3.01195 0.491400 2.38146 2 0 -2.99362 0.00000 2.39881 2 0 -2.97579 0.473937 2.32807 2 0 +3.03103 0.00000 2.44672 2 0 +3.01195 0.491400 2.38146 2 0 -3.44090 0.00000 2.15145 2 0 -3.41280 0.440287 2.09602 2 0 +3.49701 0.00000 2.21281 2 0 +3.46705 0.457130 2.15888 2 0 3.66671 0.00000 2.49441 2 0 3.64842 0.516335 2.45278 2 0 @@ -6025,23 +6025,23 @@ DEAL:3d::quarter_hyper_ball 3.14805 0.00000 2.77164 2 0 3.13894 0.554830 2.71937 2 0 -3.44090 0.00000 2.15145 2 0 -3.85616 0.00000 1.85616 2 0 +3.49701 0.00000 2.21281 2 0 +3.93097 0.00000 1.93097 2 0 4.12132 0.00000 2.12132 2 0 3.66671 0.00000 2.49441 2 0 -3.44090 0.00000 2.15145 2 0 +3.49701 0.00000 2.21281 2 0 -3.41280 0.440287 2.09602 2 0 -3.81900 0.397611 1.81900 2 0 +3.46705 0.457130 2.15888 2 0 +3.89133 0.413835 1.89133 2 0 4.09626 0.459790 2.09626 2 0 3.64842 0.516335 2.45278 2 0 -3.41280 0.440287 2.09602 2 0 +3.46705 0.457130 2.15888 2 0 -3.44090 0.00000 2.15145 2 0 -3.41280 0.440287 2.09602 2 0 +3.49701 0.00000 2.21281 2 0 +3.46705 0.457130 2.15888 2 0 -3.85616 0.00000 1.85616 2 0 -3.81900 0.397611 1.81900 2 0 +3.93097 0.00000 1.93097 2 0 +3.89133 0.413835 1.89133 2 0 4.12132 0.00000 2.12132 2 0 4.09626 0.459790 2.09626 2 0 @@ -6049,23 +6049,23 @@ DEAL:3d::quarter_hyper_ball 3.66671 0.00000 2.49441 2 0 3.64842 0.516335 2.45278 2 0 -2.97579 0.473937 2.32807 2 0 -3.41280 0.440287 2.09602 2 0 +3.01195 0.491400 2.38146 2 0 +3.46705 0.457130 2.15888 2 0 3.64842 0.516335 2.45278 2 0 3.13894 0.554830 2.71937 2 0 -2.97579 0.473937 2.32807 2 0 +3.01195 0.491400 2.38146 2 0 -2.93830 0.938299 2.21039 2 0 -3.36104 0.872621 2.00345 2 0 +2.97323 0.973225 2.26927 2 0 +3.41343 0.906307 2.06781 2 0 3.58279 1.01676 2.33687 2 0 3.09051 1.09051 2.57324 2 0 -2.93830 0.938299 2.21039 2 0 +2.97323 0.973225 2.26927 2 0 -2.97579 0.473937 2.32807 2 0 -2.93830 0.938299 2.21039 2 0 +3.01195 0.491400 2.38146 2 0 +2.97323 0.973225 2.26927 2 0 -3.41280 0.440287 2.09602 2 0 -3.36104 0.872621 2.00345 2 0 +3.46705 0.457130 2.15888 2 0 +3.41343 0.906307 2.06781 2 0 3.64842 0.516335 2.45278 2 0 3.58279 1.01676 2.33687 2 0 @@ -6073,23 +6073,23 @@ DEAL:3d::quarter_hyper_ball 3.13894 0.554830 2.71937 2 0 3.09051 1.09051 2.57324 2 0 -3.41280 0.440287 2.09602 2 0 -3.81900 0.397611 1.81900 2 0 +3.46705 0.457130 2.15888 2 0 +3.89133 0.413835 1.89133 2 0 4.09626 0.459790 2.09626 2 0 3.64842 0.516335 2.45278 2 0 -3.41280 0.440287 2.09602 2 0 +3.46705 0.457130 2.15888 2 0 -3.36104 0.872621 2.00345 2 0 -3.75708 0.789790 1.75708 2 0 +3.41343 0.906307 2.06781 2 0 +3.82693 0.822237 1.82693 2 0 4.02166 0.908716 2.02166 2 0 3.58279 1.01676 2.33687 2 0 -3.36104 0.872621 2.00345 2 0 +3.41343 0.906307 2.06781 2 0 -3.41280 0.440287 2.09602 2 0 -3.36104 0.872621 2.00345 2 0 +3.46705 0.457130 2.15888 2 0 +3.41343 0.906307 2.06781 2 0 -3.81900 0.397611 1.81900 2 0 -3.75708 0.789790 1.75708 2 0 +3.89133 0.413835 1.89133 2 0 +3.82693 0.822237 1.82693 2 0 4.09626 0.459790 2.09626 2 0 4.02166 0.908716 2.02166 2 0 @@ -6097,119 +6097,119 @@ DEAL:3d::quarter_hyper_ball 3.64842 0.516335 2.45278 2 0 3.58279 1.01676 2.33687 2 0 -2.00000 0.839190 2.02598 2 0 -2.39305 0.812640 1.93676 2 0 -2.47394 0.975788 2.32807 2 0 -2.00000 0.993620 2.39881 2 0 -2.00000 0.839190 2.02598 2 0 +2.00000 0.914000 2.12179 2 0 +2.42797 0.884971 2.04355 2 0 +2.49140 1.01195 2.38146 2 0 +2.00000 1.03103 2.44672 2 0 +2.00000 0.914000 2.12179 2 0 -2.00000 1.21509 1.80849 2 0 -2.36424 1.17719 1.73925 2 0 -2.44029 1.41280 2.09602 2 0 -2.00000 1.44090 2.15145 2 0 -2.00000 1.21509 1.80849 2 0 +2.00000 1.32731 1.93120 2 0 +2.39792 1.28569 1.86498 2 0 +2.45713 1.46705 2.15888 2 0 +2.00000 1.49701 2.21281 2 0 +2.00000 1.32731 1.93120 2 0 -2.00000 0.839190 2.02598 2 0 -2.00000 1.21509 1.80849 2 0 +2.00000 0.914000 2.12179 2 0 +2.00000 1.32731 1.93120 2 0 -2.39305 0.812640 1.93676 2 0 -2.36424 1.17719 1.73925 2 0 +2.42797 0.884971 2.04355 2 0 +2.39792 1.28569 1.86498 2 0 -2.47394 0.975788 2.32807 2 0 -2.44029 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1.01195 2.38146 2 0 +2.45713 1.46705 2.15888 2 0 2.55483 1.13894 2.71937 2 0 2.51634 1.64842 2.45278 2 0 @@ -6217,23 +6217,23 @@ DEAL:3d::quarter_hyper_ball 2.00000 1.14805 2.77164 2 0 2.00000 1.66671 2.49441 2 0 -2.47394 0.975788 2.32807 2 0 -2.93830 0.938299 2.21039 2 0 +2.49140 1.01195 2.38146 2 0 +2.97323 0.973225 2.26927 2 0 3.09051 1.09051 2.57324 2 0 2.55483 1.13894 2.71937 2 0 -2.47394 0.975788 2.32807 2 0 +2.49140 1.01195 2.38146 2 0 -2.44029 1.41280 2.09602 2 0 -2.87262 1.36104 2.00345 2 0 +2.45713 1.46705 2.15888 2 0 +2.90631 1.41343 2.06781 2 0 3.01676 1.58279 2.33687 2 0 2.51634 1.64842 2.45278 2 0 -2.44029 1.41280 2.09602 2 0 +2.45713 1.46705 2.15888 2 0 -2.47394 0.975788 2.32807 2 0 -2.44029 1.41280 2.09602 2 0 +2.49140 1.01195 2.38146 2 0 +2.45713 1.46705 2.15888 2 0 -2.93830 0.938299 2.21039 2 0 -2.87262 1.36104 2.00345 2 0 +2.97323 0.973225 2.26927 2 0 +2.90631 1.41343 2.06781 2 0 3.09051 1.09051 2.57324 2 0 3.01676 1.58279 2.33687 2 0 @@ -6241,23 +6241,23 @@ DEAL:3d::quarter_hyper_ball 2.55483 1.13894 2.71937 2 0 2.51634 1.64842 2.45278 2 0 -2.00000 1.44090 2.15145 2 0 -2.44029 1.41280 2.09602 2 0 +2.00000 1.49701 2.21281 2 0 +2.45713 1.46705 2.15888 2 0 2.51634 1.64842 2.45278 2 0 2.00000 1.66671 2.49441 2 0 -2.00000 1.44090 2.15145 2 0 +2.00000 1.49701 2.21281 2 0 -2.00000 1.85616 1.85616 2 0 -2.39761 1.81900 1.81900 2 0 +2.00000 1.93097 1.93097 2 0 +2.41383 1.89133 1.89133 2 0 2.45979 2.09626 2.09626 2 0 2.00000 2.12132 2.12132 2 0 -2.00000 1.85616 1.85616 2 0 +2.00000 1.93097 1.93097 2 0 -2.00000 1.44090 2.15145 2 0 -2.00000 1.85616 1.85616 2 0 +2.00000 1.49701 2.21281 2 0 +2.00000 1.93097 1.93097 2 0 -2.44029 1.41280 2.09602 2 0 -2.39761 1.81900 1.81900 2 0 +2.45713 1.46705 2.15888 2 0 +2.41383 1.89133 1.89133 2 0 2.51634 1.64842 2.45278 2 0 2.45979 2.09626 2.09626 2 0 @@ -6265,23 +6265,23 @@ DEAL:3d::quarter_hyper_ball 2.00000 1.66671 2.49441 2 0 2.00000 2.12132 2.12132 2 0 -2.44029 1.41280 2.09602 2 0 -2.87262 1.36104 2.00345 2 0 +2.45713 1.46705 2.15888 2 0 +2.90631 1.41343 2.06781 2 0 3.01676 1.58279 2.33687 2 0 2.51634 1.64842 2.45278 2 0 -2.44029 1.41280 2.09602 2 0 +2.45713 1.46705 2.15888 2 0 -2.39761 1.81900 1.81900 2 0 -2.78979 1.75708 1.75708 2 0 +2.41383 1.89133 1.89133 2 0 +2.82224 1.82693 1.82693 2 0 2.90872 2.02166 2.02166 2 0 2.45979 2.09626 2.09626 2 0 -2.39761 1.81900 1.81900 2 0 +2.41383 1.89133 1.89133 2 0 -2.44029 1.41280 2.09602 2 0 -2.39761 1.81900 1.81900 2 0 +2.45713 1.46705 2.15888 2 0 +2.41383 1.89133 1.89133 2 0 -2.87262 1.36104 2.00345 2 0 -2.78979 1.75708 1.75708 2 0 +2.90631 1.41343 2.06781 2 0 +2.82224 1.82693 1.82693 2 0 3.01676 1.58279 2.33687 2 0 2.90872 2.02166 2.02166 2 0 @@ -6289,119 +6289,119 @@ DEAL:3d::quarter_hyper_ball 2.51634 1.64842 2.45278 2 0 2.45979 2.09626 2.09626 2 0 -2.78609 0.786090 1.84754 2 0 -3.13930 0.728477 1.67002 2 0 -3.36104 0.872621 2.00345 2 0 -2.93830 0.938299 2.21039 2 0 -2.78609 0.786090 1.84754 2 0 +2.85594 0.855942 1.96530 2 0 +3.24407 0.795850 1.79875 2 0 +3.41343 0.906307 2.06781 2 0 +2.97323 0.973225 2.26927 2 0 +2.85594 0.855942 1.96530 2 0 -2.72848 1.13930 1.67002 2 0 -3.06212 1.06212 1.53290 2 0 -3.27100 1.27100 1.84115 2 0 -2.87262 1.36104 2.00345 2 0 -2.72848 1.13930 1.67002 2 0 +2.79585 1.24407 1.79875 2 0 +3.16318 1.16318 1.66463 2 0 +3.32153 1.32153 1.90702 2 0 +2.90631 1.41343 2.06781 2 0 +2.79585 1.24407 1.79875 2 0 -2.78609 0.786090 1.84754 2 0 -2.72848 1.13930 1.67002 2 0 +2.85594 0.855942 1.96530 2 0 +2.79585 1.24407 1.79875 2 0 -3.13930 0.728477 1.67002 2 0 -3.06212 1.06212 1.53290 2 0 +3.24407 0.795850 1.79875 2 0 +3.16318 1.16318 1.66463 2 0 -3.36104 0.872621 2.00345 2 0 -3.27100 1.27100 1.84115 2 0 +3.41343 0.906307 2.06781 2 0 +3.32153 1.32153 1.90702 2 0 -2.93830 0.938299 2.21039 2 0 -2.87262 1.36104 2.00345 2 0 +2.97323 0.973225 2.26927 2 0 +2.90631 1.41343 2.06781 2 0 -3.13930 0.728477 1.67002 2 0 -3.49250 0.670865 1.49250 2 0 -3.75708 0.789790 1.75708 2 0 -3.36104 0.872621 2.00345 2 0 -3.13930 0.728477 1.67002 2 0 +3.24407 0.795850 1.79875 2 0 +3.63221 0.735758 1.63221 2 0 +3.82693 0.822237 1.82693 2 0 +3.41343 0.906307 2.06781 2 0 +3.24407 0.795850 1.79875 2 0 -3.06212 1.06212 1.53290 2 0 -3.39577 0.984951 1.39577 2 0 -3.64753 1.16056 1.64753 2 0 -3.27100 1.27100 1.84115 2 0 -3.06212 1.06212 1.53290 2 0 +3.16318 1.16318 1.66463 2 0 +3.53052 1.08229 1.53052 2 0 +3.71491 1.20923 1.71491 2 0 +3.32153 1.32153 1.90702 2 0 +3.16318 1.16318 1.66463 2 0 -3.13930 0.728477 1.67002 2 0 -3.06212 1.06212 1.53290 2 0 +3.24407 0.795850 1.79875 2 0 +3.16318 1.16318 1.66463 2 0 -3.49250 0.670865 1.49250 2 0 -3.39577 0.984951 1.39577 2 0 +3.63221 0.735758 1.63221 2 0 +3.53052 1.08229 1.53052 2 0 -3.75708 0.789790 1.75708 2 0 -3.64753 1.16056 1.64753 2 0 +3.82693 0.822237 1.82693 2 0 +3.71491 1.20923 1.71491 2 0 -3.36104 0.872621 2.00345 2 0 -3.27100 1.27100 1.84115 2 0 +3.41343 0.906307 2.06781 2 0 +3.32153 1.32153 1.90702 2 0 -2.72848 1.13930 1.67002 2 0 -3.06212 1.06212 1.53290 2 0 -3.27100 1.27100 1.84115 2 0 -2.87262 1.36104 2.00345 2 0 -2.72848 1.13930 1.67002 2 0 +2.79585 1.24407 1.79875 2 0 +3.16318 1.16318 1.66463 2 0 +3.32153 1.32153 1.90702 2 0 +2.90631 1.41343 2.06781 2 0 +2.79585 1.24407 1.79875 2 0 -2.67086 1.49250 1.49250 2 0 -2.98495 1.39577 1.39577 2 0 -3.16056 1.64753 1.64753 2 0 -2.78979 1.75708 1.75708 2 0 -2.67086 1.49250 1.49250 2 0 +2.73576 1.63221 1.63221 2 0 +3.08229 1.53052 1.53052 2 0 +3.20923 1.71491 1.71491 2 0 +2.82224 1.82693 1.82693 2 0 +2.73576 1.63221 1.63221 2 0 -2.72848 1.13930 1.67002 2 0 -2.67086 1.49250 1.49250 2 0 +2.79585 1.24407 1.79875 2 0 +2.73576 1.63221 1.63221 2 0 -3.06212 1.06212 1.53290 2 0 -2.98495 1.39577 1.39577 2 0 +3.16318 1.16318 1.66463 2 0 +3.08229 1.53052 1.53052 2 0 -3.27100 1.27100 1.84115 2 0 -3.16056 1.64753 1.64753 2 0 +3.32153 1.32153 1.90702 2 0 +3.20923 1.71491 1.71491 2 0 -2.87262 1.36104 2.00345 2 0 -2.78979 1.75708 1.75708 2 0 +2.90631 1.41343 2.06781 2 0 +2.82224 1.82693 1.82693 2 0 -3.06212 1.06212 1.53290 2 0 -3.39577 0.984951 1.39577 2 0 -3.64753 1.16056 1.64753 2 0 -3.27100 1.27100 1.84115 2 0 -3.06212 1.06212 1.53290 2 0 +3.16318 1.16318 1.66463 2 0 +3.53052 1.08229 1.53052 2 0 +3.71491 1.20923 1.71491 2 0 +3.32153 1.32153 1.90702 2 0 +3.16318 1.16318 1.66463 2 0 -2.98495 1.39577 1.39577 2 0 -3.29904 1.29904 1.29904 2 0 -3.51554 1.51554 1.51554 2 0 -3.16056 1.64753 1.64753 2 0 -2.98495 1.39577 1.39577 2 0 +3.08229 1.53052 1.53052 2 0 +3.42883 1.42883 1.42883 2 0 +3.58044 1.58044 1.58044 2 0 +3.20923 1.71491 1.71491 2 0 +3.08229 1.53052 1.53052 2 0 -3.06212 1.06212 1.53290 2 0 -2.98495 1.39577 1.39577 2 0 +3.16318 1.16318 1.66463 2 0 +3.08229 1.53052 1.53052 2 0 -3.39577 0.984951 1.39577 2 0 -3.29904 1.29904 1.29904 2 0 +3.53052 1.08229 1.53052 2 0 +3.42883 1.42883 1.42883 2 0 -3.64753 1.16056 1.64753 2 0 -3.51554 1.51554 1.51554 2 0 +3.71491 1.20923 1.71491 2 0 +3.58044 1.58044 1.58044 2 0 -3.27100 1.27100 1.84115 2 0 -3.16056 1.64753 1.64753 2 0 +3.32153 1.32153 1.90702 2 0 +3.20923 1.71491 1.71491 2 0 -2.93830 0.938299 2.21039 2 0 -3.36104 0.872621 2.00345 2 0 +2.97323 0.973225 2.26927 2 0 +3.41343 0.906307 2.06781 2 0 3.58279 1.01676 2.33687 2 0 3.09051 1.09051 2.57324 2 0 -2.93830 0.938299 2.21039 2 0 +2.97323 0.973225 2.26927 2 0 -2.87262 1.36104 2.00345 2 0 -3.27100 1.27100 1.84115 2 0 +2.90631 1.41343 2.06781 2 0 +3.32153 1.32153 1.90702 2 0 3.47988 1.47988 2.14940 2 0 3.01676 1.58279 2.33687 2 0 -2.87262 1.36104 2.00345 2 0 +2.90631 1.41343 2.06781 2 0 -2.93830 0.938299 2.21039 2 0 -2.87262 1.36104 2.00345 2 0 +2.97323 0.973225 2.26927 2 0 +2.90631 1.41343 2.06781 2 0 -3.36104 0.872621 2.00345 2 0 -3.27100 1.27100 1.84115 2 0 +3.41343 0.906307 2.06781 2 0 +3.32153 1.32153 1.90702 2 0 3.58279 1.01676 2.33687 2 0 3.47988 1.47988 2.14940 2 0 @@ -6409,23 +6409,23 @@ DEAL:3d::quarter_hyper_ball 3.09051 1.09051 2.57324 2 0 3.01676 1.58279 2.33687 2 0 -3.36104 0.872621 2.00345 2 0 -3.75708 0.789790 1.75708 2 0 +3.41343 0.906307 2.06781 2 0 +3.82693 0.822237 1.82693 2 0 4.02166 0.908716 2.02166 2 0 3.58279 1.01676 2.33687 2 0 -3.36104 0.872621 2.00345 2 0 +3.41343 0.906307 2.06781 2 0 -3.27100 1.27100 1.84115 2 0 -3.64753 1.16056 1.64753 2 0 +3.32153 1.32153 1.90702 2 0 +3.71491 1.20923 1.71491 2 0 3.89930 1.33617 1.89930 2 0 3.47988 1.47988 2.14940 2 0 -3.27100 1.27100 1.84115 2 0 +3.32153 1.32153 1.90702 2 0 -3.36104 0.872621 2.00345 2 0 -3.27100 1.27100 1.84115 2 0 +3.41343 0.906307 2.06781 2 0 +3.32153 1.32153 1.90702 2 0 -3.75708 0.789790 1.75708 2 0 -3.64753 1.16056 1.64753 2 0 +3.82693 0.822237 1.82693 2 0 +3.71491 1.20923 1.71491 2 0 4.02166 0.908716 2.02166 2 0 3.89930 1.33617 1.89930 2 0 @@ -6433,23 +6433,23 @@ DEAL:3d::quarter_hyper_ball 3.58279 1.01676 2.33687 2 0 3.47988 1.47988 2.14940 2 0 -2.87262 1.36104 2.00345 2 0 -3.27100 1.27100 1.84115 2 0 +2.90631 1.41343 2.06781 2 0 +3.32153 1.32153 1.90702 2 0 3.47988 1.47988 2.14940 2 0 3.01676 1.58279 2.33687 2 0 -2.87262 1.36104 2.00345 2 0 +2.90631 1.41343 2.06781 2 0 -2.78979 1.75708 1.75708 2 0 -3.16056 1.64753 1.64753 2 0 +2.82224 1.82693 1.82693 2 0 +3.20923 1.71491 1.71491 2 0 3.33617 1.89930 1.89930 2 0 2.90872 2.02166 2.02166 2 0 -2.78979 1.75708 1.75708 2 0 +2.82224 1.82693 1.82693 2 0 -2.87262 1.36104 2.00345 2 0 -2.78979 1.75708 1.75708 2 0 +2.90631 1.41343 2.06781 2 0 +2.82224 1.82693 1.82693 2 0 -3.27100 1.27100 1.84115 2 0 -3.16056 1.64753 1.64753 2 0 +3.32153 1.32153 1.90702 2 0 +3.20923 1.71491 1.71491 2 0 3.47988 1.47988 2.14940 2 0 3.33617 1.89930 1.89930 2 0 @@ -6457,23 +6457,23 @@ DEAL:3d::quarter_hyper_ball 3.01676 1.58279 2.33687 2 0 2.90872 2.02166 2.02166 2 0 -3.27100 1.27100 1.84115 2 0 -3.64753 1.16056 1.64753 2 0 +3.32153 1.32153 1.90702 2 0 +3.71491 1.20923 1.71491 2 0 3.89930 1.33617 1.89930 2 0 3.47988 1.47988 2.14940 2 0 -3.27100 1.27100 1.84115 2 0 +3.32153 1.32153 1.90702 2 0 -3.16056 1.64753 1.64753 2 0 -3.51554 1.51554 1.51554 2 0 +3.20923 1.71491 1.71491 2 0 +3.58044 1.58044 1.58044 2 0 3.73205 1.73205 1.73205 2 0 3.33617 1.89930 1.89930 2 0 -3.16056 1.64753 1.64753 2 0 +3.20923 1.71491 1.71491 2 0 -3.27100 1.27100 1.84115 2 0 -3.16056 1.64753 1.64753 2 0 +3.32153 1.32153 1.90702 2 0 +3.20923 1.71491 1.71491 2 0 -3.64753 1.16056 1.64753 2 0 -3.51554 1.51554 1.51554 2 0 +3.71491 1.20923 1.71491 2 0 +3.58044 1.58044 1.58044 2 0 3.89930 1.33617 1.89930 2 0 3.73205 1.73205 1.73205 2 0 -- 2.39.5