/*-------------------------------------------------------------------
Copyright 2011 Ravishankar Sundararaman

This file is part of JDFTx.

JDFTx is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

JDFTx is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with JDFTx.  If not, see <http://www.gnu.org/licenses/>.
-------------------------------------------------------------------*/

#include <fluid/S2quad.h>
#include <fluid/Euler.h>
#include <algorithm>
#include <gsl/gsl_integration.h>

void S2quad::add(vector3<> n, double relWeight, double s1phase)
{	//Add the euler angle
	vector3<> tmpEuler;
	getEulerAxis(n, tmpEuler); //polar angles of S2 sets first two euler angles
	tmpEuler[2] = s1phase; //S1 phase guess is the third euler angle
	euler.push_back(tmpEuler);
	//Add the weight
	assert(relWeight > 0.);
	weight.push_back(relWeight);
}


EulerProduct::EulerProduct(unsigned nBeta, unsigned nAlphaIn, unsigned nGammaIn)
: nBeta(nBeta),
nAlpha(nAlphaIn ? nAlphaIn : 2*nBeta),
nGamma(nGammaIn ? nGammaIn : 2*nBeta)
{
	assert(nBeta>0);
	
	//Create a nBeta-point Gauss-Legendre quadrature for cos(beta) in [-1,1]
	gsl_integration_glfixed_table* glTable = gsl_integration_glfixed_table_alloc(nBeta);
	for(unsigned iBeta=0; iBeta<nBeta; iBeta++)
	{	double x, w; gsl_integration_glfixed_point(-1., +1., iBeta, &x, &w, glTable);
		double beta = acos(x); //note integration is ~ f(cos(beta)) sin(beta) dbeta
		//Create the S2 quadrature by using a uniform quadrature on alpha (since it's also S1)
		for(unsigned iAlpha=0; iAlpha<nAlpha; iAlpha++)
		{	double alpha = iAlpha * 2*M_PI/nAlpha;
			add(polarUnitVector(alpha, beta), w);
		}
	}
	gsl_integration_glfixed_table_free(glTable);
}

int EulerProduct::jMax() const
{	return std::min( 2*nBeta, std::min(nAlpha, nGamma) ) - 1;
}

int EulerProduct::nS1() const
{	return nGamma;
}

string EulerProduct::name() const
{	ostringstream oss;
	oss << "Euler(" << nBeta << "x" << nAlpha << ")";
	return oss.str();
}


//--------------- Platonic Solid rotation groups ------------------

Tetrahedron::Tetrahedron()
{	add(polarUnitVector(0.0, 0.0));
	for(int i=1; i<=3; i++) add(polarUnitVector(2*i*M_PI/3, acos(-1.0/3)), 1., M_PI/3);
}

Octahedron::Octahedron()
{	add(polarUnitVector(0.0, 0.0));
	for(int i=1; i<=4; i++) add(polarUnitVector(2*i*M_PI/4, M_PI/2));
	add(polarUnitVector(0.0, M_PI));
}

Icosahedron::Icosahedron()
{	add(polarUnitVector(0.0, 0.0));
	for(int i=1; i<=5; i++) add(polarUnitVector(2*i*M_PI/5, atan(2)), 1., M_PI/5);
	for(int i=1; i<=5; i++) add(polarUnitVector((2*i+1)*M_PI/5, M_PI-atan(2)));
	add(polarUnitVector(0.0, M_PI));
}


//--------------- Hardin and Sloane Spherical designs -----------------
// Auto-converted from http://www2.research.att.com/~njas/sphdesigns

S2_7design_24::S2_7design_24()
{	add(vector3<>(+0.866246818107821, +0.422518653761112, +0.266635401516705));
	add(vector3<>(+0.866246818107821, -0.422518653761112, -0.266635401516705));
	add(vector3<>(+0.866246818107821, +0.266635401516705, -0.422518653761112));
	add(vector3<>(+0.866246818107821, -0.266635401516705, +0.422518653761112));
	add(vector3<>(-0.866246818107821, +0.422518653761112, -0.266635401516705));
	add(vector3<>(-0.866246818107821, -0.422518653761112, +0.266635401516705));
	add(vector3<>(-0.866246818107821, +0.266635401516705, +0.422518653761112));
	add(vector3<>(-0.866246818107821, -0.266635401516705, -0.422518653761112));
	add(vector3<>(+0.266635401516705, +0.866246818107821, +0.422518653761112));
	add(vector3<>(-0.266635401516705, +0.866246818107821, -0.422518653761112));
	add(vector3<>(-0.422518653761112, +0.866246818107821, +0.266635401516705));
	add(vector3<>(+0.422518653761112, +0.866246818107821, -0.266635401516705));
	add(vector3<>(-0.266635401516705, -0.866246818107821, +0.422518653761112));
	add(vector3<>(+0.266635401516705, -0.866246818107821, -0.422518653761112));
	add(vector3<>(+0.422518653761112, -0.866246818107821, +0.266635401516705));
	add(vector3<>(-0.422518653761112, -0.866246818107821, -0.266635401516705));
	add(vector3<>(+0.422518653761112, +0.266635401516705, +0.866246818107821));
	add(vector3<>(-0.422518653761112, -0.266635401516705, +0.866246818107821));
	add(vector3<>(+0.266635401516705, -0.422518653761112, +0.866246818107821));
	add(vector3<>(-0.266635401516705, +0.422518653761112, +0.866246818107821));
	add(vector3<>(+0.422518653761112, -0.266635401516705, -0.866246818107821));
	add(vector3<>(-0.422518653761112, +0.266635401516705, -0.866246818107821));
	add(vector3<>(+0.266635401516705, +0.422518653761112, -0.866246818107821));
	add(vector3<>(-0.266635401516705, -0.422518653761112, -0.866246818107821));
}

S2_8design_36::S2_8design_36()
{	add(vector3<>(+0.507475446410817, -0.306200013239571, +0.805425492011663));
	add(vector3<>(-0.306200013239569, +0.805425492011663, +0.507475446410817));
	add(vector3<>(-0.507475446410817, +0.306200013239570, +0.805425492011663));
	add(vector3<>(+0.805425492011663, +0.507475446410817, -0.306200013239569));
	add(vector3<>(+0.306200013239569, +0.805425492011664, -0.507475446410817));
	add(vector3<>(+0.805425492011663, -0.507475446410817, +0.306200013239569));
	add(vector3<>(+0.306200013239569, -0.805425492011663, +0.507475446410816));
	add(vector3<>(-0.805425492011663, -0.507475446410817, -0.306200013239569));
	add(vector3<>(-0.306200013239570, -0.805425492011664, -0.507475446410816));
	add(vector3<>(-0.805425492011663, +0.507475446410818, +0.306200013239569));
	add(vector3<>(+0.507475446410817, +0.306200013239570, -0.805425492011663));
	add(vector3<>(-0.507475446410817, -0.306200013239570, -0.805425492011663));
	add(vector3<>(+0.626363670265271, -0.243527775409194, -0.740515209280720));
	add(vector3<>(-0.243527775409195, -0.740515209280720, +0.626363670265271));
	add(vector3<>(-0.626363670265271, +0.243527775409194, -0.740515209280720));
	add(vector3<>(-0.740515209280720, +0.626363670265270, -0.243527775409195));
	add(vector3<>(+0.243527775409195, -0.740515209280719, -0.626363670265271));
	add(vector3<>(-0.740515209280720, -0.626363670265270, +0.243527775409195));
	add(vector3<>(+0.243527775409195, +0.740515209280719, +0.626363670265271));
	add(vector3<>(+0.740515209280720, -0.626363670265270, -0.243527775409195));
	add(vector3<>(-0.243527775409195, +0.740515209280720, -0.626363670265271));
	add(vector3<>(+0.740515209280720, +0.626363670265270, +0.243527775409195));
	add(vector3<>(+0.626363670265271, +0.243527775409194, +0.740515209280720));
	add(vector3<>(-0.626363670265271, -0.243527775409194, +0.740515209280720));
	add(vector3<>(-0.286248723426035, +0.957120327092458, -0.044523564585421));
	add(vector3<>(+0.957120327092458, -0.044523564585420, -0.286248723426035));
	add(vector3<>(+0.286248723426035, -0.957120327092458, -0.044523564585421));
	add(vector3<>(-0.044523564585420, -0.286248723426035, +0.957120327092458));
	add(vector3<>(-0.957120327092458, -0.044523564585419, +0.286248723426035));
	add(vector3<>(-0.044523564585421, +0.286248723426034, -0.957120327092458));
	add(vector3<>(-0.957120327092458, +0.044523564585420, -0.286248723426034));
	add(vector3<>(+0.044523564585421, +0.286248723426034, +0.957120327092458));
	add(vector3<>(+0.957120327092458, +0.044523564585420, +0.286248723426034));
	add(vector3<>(+0.044523564585421, -0.286248723426034, -0.957120327092458));
	add(vector3<>(-0.286248723426034, -0.957120327092458, +0.044523564585421));
	add(vector3<>(+0.286248723426035, +0.957120327092458, +0.044523564585421));
}

S2_9design_48::S2_9design_48()
{	add(vector3<>(+0.933364693199310, +0.353542188921472, -0.061953774231860));
	add(vector3<>(+0.933364693199310, -0.353542188921472, +0.061953774231860));
	add(vector3<>(+0.933364693199310, -0.061953774231860, -0.353542188921472));
	add(vector3<>(+0.933364693199310, +0.061953774231860, +0.353542188921472));
	add(vector3<>(-0.933364693199310, +0.353542188921472, +0.061953774231860));
	add(vector3<>(-0.933364693199310, -0.353542188921472, -0.061953774231860));
	add(vector3<>(-0.933364693199310, -0.061953774231860, +0.353542188921472));
	add(vector3<>(-0.933364693199310, +0.061953774231860, -0.353542188921472));
	add(vector3<>(-0.061953774231860, +0.933364693199310, +0.353542188921472));
	add(vector3<>(+0.061953774231860, +0.933364693199310, -0.353542188921472));
	add(vector3<>(-0.353542188921472, +0.933364693199310, -0.061953774231860));
	add(vector3<>(+0.353542188921472, +0.933364693199310, +0.061953774231860));
	add(vector3<>(+0.061953774231860, -0.933364693199310, +0.353542188921472));
	add(vector3<>(-0.061953774231860, -0.933364693199310, -0.353542188921472));
	add(vector3<>(+0.353542188921472, -0.933364693199310, -0.061953774231860));
	add(vector3<>(-0.353542188921472, -0.933364693199310, +0.061953774231860));
	add(vector3<>(+0.353542188921472, -0.061953774231860, +0.933364693199310));
	add(vector3<>(-0.353542188921472, +0.061953774231860, +0.933364693199310));
	add(vector3<>(-0.061953774231860, -0.353542188921472, +0.933364693199310));
	add(vector3<>(+0.061953774231860, +0.353542188921472, +0.933364693199310));
	add(vector3<>(+0.353542188921472, +0.061953774231860, -0.933364693199310));
	add(vector3<>(-0.353542188921472, -0.061953774231860, -0.933364693199310));
	add(vector3<>(-0.061953774231860, +0.353542188921472, -0.933364693199310));
	add(vector3<>(+0.061953774231860, -0.353542188921472, -0.933364693199310));
	add(vector3<>(+0.706841697712550, +0.639740098619792, +0.301840057965769));
	add(vector3<>(+0.706841697712550, -0.639740098619792, -0.301840057965769));
	add(vector3<>(+0.706841697712550, +0.301840057965769, -0.639740098619792));
	add(vector3<>(+0.706841697712550, -0.301840057965769, +0.639740098619792));
	add(vector3<>(-0.706841697712550, +0.639740098619792, -0.301840057965769));
	add(vector3<>(-0.706841697712550, -0.639740098619792, +0.301840057965769));
	add(vector3<>(-0.706841697712550, +0.301840057965769, +0.639740098619792));
	add(vector3<>(-0.706841697712550, -0.301840057965769, -0.639740098619792));
	add(vector3<>(+0.301840057965769, +0.706841697712550, +0.639740098619792));
	add(vector3<>(-0.301840057965769, +0.706841697712550, -0.639740098619792));
	add(vector3<>(-0.639740098619792, +0.706841697712550, +0.301840057965769));
	add(vector3<>(+0.639740098619792, +0.706841697712550, -0.301840057965769));
	add(vector3<>(-0.301840057965769, -0.706841697712550, +0.639740098619792));
	add(vector3<>(+0.301840057965769, -0.706841697712550, -0.639740098619792));
	add(vector3<>(+0.639740098619792, -0.706841697712550, +0.301840057965769));
	add(vector3<>(-0.639740098619792, -0.706841697712550, -0.301840057965769));
	add(vector3<>(+0.639740098619792, +0.301840057965769, +0.706841697712550));
	add(vector3<>(-0.639740098619792, -0.301840057965769, +0.706841697712550));
	add(vector3<>(+0.301840057965769, -0.639740098619792, +0.706841697712550));
	add(vector3<>(-0.301840057965769, +0.639740098619792, +0.706841697712550));
	add(vector3<>(+0.639740098619792, -0.301840057965769, -0.706841697712550));
	add(vector3<>(-0.639740098619792, +0.301840057965769, -0.706841697712550));
	add(vector3<>(+0.301840057965769, +0.639740098619792, -0.706841697712550));
	add(vector3<>(-0.301840057965769, -0.639740098619792, -0.706841697712550));
}

S2_10design_60::S2_10design_60()
{	add(vector3<>(-0.753828667197017, +0.545951908061260, -0.365621190026287));
	add(vector3<>(+0.545951908061258, -0.365621190026290, -0.753828667197017));
	add(vector3<>(+0.753828667197016, -0.545951908061261, -0.365621190026288));
	add(vector3<>(-0.365621190026289, -0.753828667197017, +0.545951908061259));
	add(vector3<>(-0.545951908061258, -0.365621190026288, +0.753828667197018));
	add(vector3<>(-0.365621190026289, +0.753828667197017, -0.545951908061259));
	add(vector3<>(-0.545951908061258, +0.365621190026289, -0.753828667197017));
	add(vector3<>(+0.365621190026287, +0.753828667197017, +0.545951908061260));
	add(vector3<>(+0.545951908061259, +0.365621190026289, +0.753828667197017));
	add(vector3<>(+0.365621190026287, -0.753828667197018, -0.545951908061259));
	add(vector3<>(-0.753828667197017, -0.545951908061261, +0.365621190026288));
	add(vector3<>(+0.753828667197016, +0.545951908061261, +0.365621190026287));
	add(vector3<>(+0.700181019363730, -0.713151065847793, +0.034089549761256));
	add(vector3<>(-0.713151065847794, +0.034089549761254, +0.700181019363729));
	add(vector3<>(-0.700181019363730, +0.713151065847793, +0.034089549761256));
	add(vector3<>(+0.034089549761255, +0.700181019363730, -0.713151065847793));
	add(vector3<>(+0.713151065847793, +0.034089549761254, -0.700181019363730));
	add(vector3<>(+0.034089549761257, -0.700181019363729, +0.713151065847794));
	add(vector3<>(+0.713151065847794, -0.034089549761255, +0.700181019363728));
	add(vector3<>(-0.034089549761256, -0.700181019363729, -0.713151065847794));
	add(vector3<>(-0.713151065847794, -0.034089549761254, -0.700181019363729));
	add(vector3<>(-0.034089549761257, +0.700181019363729, +0.713151065847794));
	add(vector3<>(+0.700181019363730, +0.713151065847793, -0.034089549761257));
	add(vector3<>(-0.700181019363729, -0.713151065847794, -0.034089549761257));
	add(vector3<>(+0.276230218261792, +0.077050720725736, -0.957997939953259));
	add(vector3<>(+0.077050720725735, -0.957997939953258, +0.276230218261793));
	add(vector3<>(-0.276230218261792, -0.077050720725734, -0.957997939953259));
	add(vector3<>(-0.957997939953259, +0.276230218261791, +0.077050720725738));
	add(vector3<>(-0.077050720725735, -0.957997939953259, -0.276230218261792));
	add(vector3<>(-0.957997939953258, -0.276230218261793, -0.077050720725736));
	add(vector3<>(-0.077050720725736, +0.957997939953258, +0.276230218261794));
	add(vector3<>(+0.957997939953259, -0.276230218261790, +0.077050720725737));
	add(vector3<>(+0.077050720725734, +0.957997939953259, -0.276230218261792));
	add(vector3<>(+0.957997939953258, +0.276230218261793, -0.077050720725738));
	add(vector3<>(+0.276230218261793, -0.077050720725736, +0.957997939953258));
	add(vector3<>(-0.276230218261791, +0.077050720725735, +0.957997939953259));
	add(vector3<>(+0.451819102555243, -0.783355937521819, +0.426864116219070));
	add(vector3<>(-0.783355937521818, +0.426864116219071, +0.451819102555243));
	add(vector3<>(-0.451819102555243, +0.783355937521819, +0.426864116219070));
	add(vector3<>(+0.426864116219071, +0.451819102555242, -0.783355937521819));
	add(vector3<>(+0.783355937521818, +0.426864116219070, -0.451819102555244));
	add(vector3<>(+0.426864116219072, -0.451819102555242, +0.783355937521818));
	add(vector3<>(+0.783355937521819, -0.426864116219070, +0.451819102555242));
	add(vector3<>(-0.426864116219072, -0.451819102555241, -0.783355937521819));
	add(vector3<>(-0.783355937521818, -0.426864116219070, -0.451819102555243));
	add(vector3<>(-0.426864116219072, +0.451819102555241, +0.783355937521819));
	add(vector3<>(+0.451819102555243, +0.783355937521818, -0.426864116219071));
	add(vector3<>(-0.451819102555242, -0.783355937521819, -0.426864116219071));
	add(vector3<>(-0.338584359959260, -0.933210037239527, +0.120331448866784));
	add(vector3<>(-0.933210037239526, +0.120331448866787, -0.338584359959260));
	add(vector3<>(+0.338584359959261, +0.933210037239526, +0.120331448866786));
	add(vector3<>(+0.120331448866785, -0.338584359959261, -0.933210037239526));
	add(vector3<>(+0.933210037239526, +0.120331448866789, +0.338584359959260));
	add(vector3<>(+0.120331448866785, +0.338584359959261, +0.933210037239526));
	add(vector3<>(+0.933210037239526, -0.120331448866787, -0.338584359959262));
	add(vector3<>(-0.120331448866784, +0.338584359959262, -0.933210037239526));
	add(vector3<>(-0.933210037239526, -0.120331448866787, +0.338584359959261));
	add(vector3<>(-0.120331448866784, -0.338584359959262, +0.933210037239526));
	add(vector3<>(-0.338584359959262, +0.933210037239526, -0.120331448866784));
	add(vector3<>(+0.338584359959261, -0.933210037239527, -0.120331448866783));
}

S2_11design_70::S2_11design_70()
{	add(vector3<>(-0.674940520480437, +0.725629052064501, +0.133857284499464));
	add(vector3<>(+0.096724334461430, -0.910327382989987, -0.402428203412229));
	add(vector3<>(+0.906960315916358, +0.135127022135053, +0.398953221871704));
	add(vector3<>(-0.132758704758026, -0.307658524060733, +0.942189661842955));
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	add(vector3<>(+0.099860111408803, +0.666551337869757, -0.738740327945793));
}

S2_12design_84::S2_12design_84()
{	add(vector3<>(-0.893804977761136, -0.426862191124497, +0.137482113446834));
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	add(vector3<>(+0.678701446637016, +0.729764213321344, -0.082513873308075));
}

S2_13design_94::S2_13design_94()
{	add(vector3<>(+0.276790129286922, -0.235256466916603, +0.931687511509759));
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	add(vector3<>(-0.521404384476695, +0.728039165452453, -0.445080264015126));
	add(vector3<>(-0.738099355384499, -0.407803273209131, -0.537499611107679));
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	add(vector3<>(-0.179848227916839, +0.832482785402468, +0.524048687550806));
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	add(vector3<>(-0.683629784685343, +0.219967331325312, +0.695891292258132));
	add(vector3<>(-0.256574099500943, -0.681472791069379, +0.685393731002400));
	add(vector3<>(+0.008242738783470, -0.934087059459458, +0.356950168241634));
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	add(vector3<>(+0.062273759768788, +0.944434685686016, +0.322746190244617));
	add(vector3<>(-0.939840260741931, +0.044569841801960, +0.338694277321433));
	add(vector3<>(-0.684400344460716, +0.714441044251305, +0.145499700312953));
	add(vector3<>(-0.660710489482671, -0.731357715034246, +0.169048932997096));
	add(vector3<>(+0.773611287955743, -0.615222357858877, +0.151746583282855));
	add(vector3<>(+0.691014301313431, +0.702815226889319, +0.168967429502926));
	add(vector3<>(+0.823586023578098, -0.394634588904438, +0.407393670798948));
	add(vector3<>(+0.494068620358303, +0.708839608416629, +0.503430837272612));
	add(vector3<>(-0.758875130501050, +0.450605887274021, +0.470173234734822));
	add(vector3<>(-0.431499072601357, -0.787935048711447, +0.439279989706176));
	add(vector3<>(+0.488574873974618, +0.006884557979146, +0.872494811091801));
	add(vector3<>(-0.055542048725634, +0.584131720247444, +0.809756268406810));
	add(vector3<>(-0.526812107467580, -0.049707819615904, +0.848527039106356));
	add(vector3<>(-0.004245864106237, -0.488654622389235, +0.872466980839748));
	add(vector3<>(-0.494068620357740, -0.708839608420214, -0.503430837268118));
	add(vector3<>(+0.758875130496518, -0.450605887275878, -0.470173234740358));
	add(vector3<>(+0.431499072601226, +0.787935048714215, -0.439279989701340));
	add(vector3<>(-0.823586023577754, +0.394634588903444, -0.407393670800605));
	add(vector3<>(-0.052238147878740, -0.056184830047506, -0.997052877624217));
	add(vector3<>(+0.052238147881538, +0.056184830047690, +0.997052877624060));
}

S2_14design_108::S2_14design_108()
{	add(vector3<>(-0.625520988160254, -0.767361004554400, +0.140998517936470));
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	add(vector3<>(-0.141107421738627, +0.625630007825311, -0.767252102531351));
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	add(vector3<>(-0.429341247317559, +0.715523561571074, -0.551082685436994));
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	add(vector3<>(+0.715607390634810, -0.550999938995098, -0.429307733096245));
}

S2_15design_120::S2_15design_120()
{	add(vector3<>(+0.854403279867469, -0.505354134007206, +0.120881076242474));
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	add(vector3<>(+0.120833358636621, +0.854397789834015, -0.505374827397788));
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	add(vector3<>(-0.264656934006370, -0.883897033692944, +0.385594010730408));
	add(vector3<>(+0.264708980625706, +0.883800765821330, +0.385778902883153));
	add(vector3<>(-0.973352164893031, +0.228026239253951, +0.024281624940474));
	add(vector3<>(+0.228112345886926, +0.024344549147457, -0.973330416960638));
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}

S2_16design_144::S2_16design_144()
{	add(vector3<>(+0.938311825813856, -0.175079255774920, -0.298191501782276));
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	add(vector3<>(-0.128471046150121, +0.025696657527584, -0.991380286314492));
	add(vector3<>(-0.991388770492313, +0.128433611757029, -0.025556077805202));
	add(vector3<>(+0.128434643068809, +0.025467323295080, +0.991390920829907));
	add(vector3<>(+0.991386054149539, +0.128448345934336, +0.025587380962899));
	add(vector3<>(+0.128392989158359, -0.025449752164830, -0.991396767419448));
	add(vector3<>(-0.025589705051665, -0.991398220731893, +0.128353943940207));
	add(vector3<>(+0.025571746935955, +0.991376476866512, +0.128525354986419));
}

S2_17design_156::S2_17design_156()
{	add(vector3<>(-0.053895316433783, -0.140603506676410, -0.988597971258691));
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	add(vector3<>(-0.988598065863270, +0.053892813420617, +0.140603800919506));
	add(vector3<>(+0.140601812415730, +0.988598276619905, -0.053894135205652));
	add(vector3<>(+0.988598002509875, +0.053895652551635, -0.140603158106489));
	add(vector3<>(-0.140604846635692, +0.988597850035353, +0.053894044272357));
	add(vector3<>(+0.988598167360928, -0.053892450727800, +0.140603226297146));
	add(vector3<>(-0.053892835910884, +0.140602751584219, +0.988598213878838));
	add(vector3<>(+0.053896097450443, -0.140603793852246, +0.988597887836084));
	add(vector3<>(-0.712137820619482, +0.484725955627139, +0.507839022116940));
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	add(vector3<>(-0.484727642870466, +0.507838390853387, +0.712137122338588));
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	add(vector3<>(-0.484726768067281, -0.507839236872381, -0.712137114474401));
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	add(vector3<>(+0.484728549122460, -0.507840095411427, +0.712135289926112));
	add(vector3<>(-0.507838861015403, -0.712137466171353, -0.484726645149226));
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	add(vector3<>(-0.052986574701187, -0.951905591847301, -0.301775027315507));
	add(vector3<>(-0.301776941841401, -0.052986526316734, -0.951904987591586));
	add(vector3<>(-0.052988794896112, +0.951905240176443, +0.301775746772478));
	add(vector3<>(+0.951904861812240, +0.301777462059556, -0.052985823114433));
	add(vector3<>(-0.951905018594348, -0.301776824324304, -0.052986638651951));
	add(vector3<>(+0.553606146300219, +0.454401156690480, +0.697882385203248));
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	add(vector3<>(-0.553605814018882, -0.454401128197097, +0.697882667342941));
	add(vector3<>(+0.697880969772289, +0.553607891253260, +0.454401204632875));
	add(vector3<>(-0.454400796454347, +0.697882268834231, -0.553606588678677));
	add(vector3<>(+0.697882520653254, -0.553605103541103, -0.454402219074583));
	add(vector3<>(-0.454400180900896, -0.697882141032518, +0.553607255032936));
	add(vector3<>(-0.697881635390884, -0.553607048847703, +0.454401208680482));
	add(vector3<>(+0.454401271818775, -0.697881725780630, -0.553606883077631));
	add(vector3<>(-0.697882321916330, +0.553606343141444, -0.454401014072625));
	add(vector3<>(+0.553606029480292, -0.454400306845994, -0.697883031217504));
	add(vector3<>(-0.553606960810672, +0.454400842716203, -0.697881943512493));
}

S2_18design_180::S2_18design_180()
{	add(vector3<>(-0.866376343641697, +0.223696804580225, +0.446488265017841));
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}

S2_19design_204::S2_19design_204()
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}

S2_20design_216::S2_20design_216()
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}

S2_21design_240::S2_21design_240()
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