
speed of light in vacuum c, c0 299 792 458 m s.1 (exact)
magnetic constant 0 4p ~ 10.7 N A.2
   = 12.566 370 614... ~ 10.7 N A.2 (exact)
     electric constant 1/0c2 .0 8.854 187 817... ~ 10.12 F m.1 (exact)
     Newtonian constant
     of gravitation G 6.674 28(67) ~ 10.11 m3 kg.1 s.2 1.0 ~ 10.4
     Planck constant h 6.626 068 96(33) ~ 10.34 J s 5.0 ~ 10.8
     h/2p Ph 1.054 571 628(53) ~ 10.34 J s 5.0 ~ 10.8
     elementary charge e 1.602 176 487(40) ~ 10.19 C 2.5 ~ 10.8
     magnetic flux quantum h/2e 0 2.067 833 667(52) ~ 10.15 Wb 2.5 ~ 10.8
     conductance quantum 2e2/h G0 7.748 091 7004(53) ~ 10.5 S 6.8 ~ 10.10
     electron mass me 9.109 382 15(45) ~ 10.31 kg 5.0 ~ 10.8
     proton mass mp 1.672 621 637(83) ~ 10.27 kg 5.0 ~ 10.8
     proton-electron mass ratio mp/me 1836.152 672 47(80) 4.3 ~ 10.10
     fine-structure constant e2/4p.0Phc  7.297 352 5376(50) ~ 10.3 6.8 ~ 10.10
     inverse fine-structure constant .1 137.035 999 679(94) 6.8 ~ 10.10
     Rydberg constant 2mec/2h R 10 973 731.568 527(73) m.1 6.6 ~ 10.12
     Avogadro constant NA,L 6.022 141 79(30) ~ 1023 mol.1 5.0 ~ 10.8
     Faraday constant NAe F 96 485.3399(24) C mol.1 2.5 ~ 10.8
     molar gas constant R 8.314 472(15) J mol.1 K.1 1.7 ~ 10.6
     Boltzmann constant R/NA k 1.380 6504(24) ~ 10.23 J K.1 1.7 ~ 10.6
     Stefan-Boltzmann constant
     (p2/60)k4/Ph3c2  5.670 400(40) ~ 10.8 W m.2 K.4 7.0 ~ 10.6
     Non-SI units accepted for use with the SI
     electron volt: (e/C) J eV 1.602 176 487(40) ~ 10.19 J 2.5 ~ 10.8
     (unified) atomic mass unit
     1 u = mu = 1
		12m(12C) u 1.660 538 782(83) ~ 10.27 kg 5.0 ~ 10.8
		= 10

		  speed of light in vacuum c, c0 299 792 458 m s.1 (exact)
		  magnetic constant 0 4p ~ 10.7 N A.2
		  = 12.566 370 614... ~ 10.7 N A.2 (exact)
		    electric constant 1/0c2 .0 8.854 187 817... ~ 10.12 F m.1 (exact)
		    characteristic impedance
		    of vacuum
		    p
		    0/.0 = 0c Z0 376.730 313 461... 
			     (exact)
			     Newtonian constant
			     of gravitation G 6.674 28(67) ~ 10.11 m3 kg.1 s.2 1.0 ~ 10.4
			     G/Phc 6.708 81(67) ~ 10.39 (GeV/c2).2 1.0 ~ 10.4
			     Planck constant h 6.626 068 96(33) ~ 10.34 J s 5.0 ~ 10.8
			     in eV s 4.135 667 33(10) ~ 10.15 eV s 2.5 ~ 10.8
			     h/2p Ph 1.054 571 628(53) ~ 10.34 J s 5.0 ~ 10.8
			     in eV s 6.582 118 99(16) ~ 10.16 eV s 2.5 ~ 10.8
			     Phc in MeV fm 197.326 9631(49) MeV fm 2.5 ~ 10.8
			     Planck mass (Phc/G)1/2 mP 2.176 44(11) ~ 10.8 kg 5.0 ~ 10.5
			     energy equivalent in GeV mPc2 1.220 892(61) ~ 1019 GeV 5.0 ~ 10.5
			     Planck temperature (Phc5/G)1/2/k TP 1.416 785(71) ~ 1032 K 5.0 ~ 10.5
			     Planck length Ph/mPc = (PhG/c3)1/2 lP 1.616 252(81) ~ 10.35 m 5.0 ~ 10.5
	Planck time lP/c = (PhG/c5)1/2 tP 5.391 24(27) ~ 10.44 s 5.0 ~ 10.5
			   ELECTROMAGNETIC
			   elementary charge e 1.602 176 487(40) ~ 10.19 C 2.5 ~ 10.8
			   e/h 2.417 989 454(60) ~ 1014 A J.1 2.5 ~ 10.8
			   magnetic flux quantum h/2e 0 2.067 833 667(52) ~ 10.15 Wb 2.5 ~ 10.8
			   conductance quantum 2e2/h G0 7.748 091 7004(53) ~ 10.5 S 6.8 ~ 10.10
			   inverse of conductance quantum G.1
			   0 12 906.403 7787(88) 
			   6.8 ~ 10.10
			   Josephson constanta 2e/h KJ 483 597.891(12) ~ 109 Hz V.1 2.5 ~ 10.8
			   von Klitzing constantb
			   h/e2 = 0c/2 RK 25 812.807 557(18) 
				  6.8 ~ 10.10
				  Bohr magneton ePh/2me B 927.400 915(23) ~ 10.26 J T.1 2.5 ~ 10.8
				  in eV T.1 5.788 381 7555(79) ~ 10.5 eV T.1 1.4 ~ 10.9
				  B/h 13.996 246 04(35) ~ 109 Hz T.1 2.5 ~ 10.8
				  B/hc 46.686 4515(12) m.1 T.1 2.5 ~ 10.8
				  B/k 0.671 7131(12) K T.1 1.7 ~ 10.6
				  nuclear magneton ePh/2mp N 5.050 783 24(13) ~ 10.27 J T.1 2.5 ~ 10.8
				  in eV T.1 3.152 451 2326(45) ~ 10.8 eV T.1 1.4 ~ 10.9
				  N/h 7.622 593 84(19) MHz T.1 2.5 ~ 10.8
				  N/hc 2.542 623 616(64) ~ 10.2 m.1 T.1 2.5 ~ 10.8
				  N/k 3.658 2637(64) ~ 10.4 K T.1 1.7 ~ 10.6

		  fine-structure constant e2/4p.0Phc  7.297 352 5376(50) ~ 10.3 6.8 ~ 10.10
		  inverse fine-structure constant .1 137.035 999 679(94) 6.8 ~ 10.10
		  Rydberg constant 2mec/2h R 10 973 731.568 527(73) m.1 6.6 ~ 10.12

				  Rc 3.289 841 960 361(22) ~ 1015 Hz 6.6 ~ 10.12
				  Rhc 2.179 871 97(11) ~ 10.18 J 5.0 ~ 10.8
				  Rhc in eV 13.605 691 93(34) eV 2.5 ~ 10.8
				  Bohr radius /4pR = 4p.0Ph2/mee2 a0 0.529 177 208 59(36) ~ 10.10 m 6.8 ~ 10.10
	Hartree energy e2/4p.0a0 = 2Rhc
				   = 2mec2 Eh 4.359 743 94(22) ~ 10.18 J 5.0 ~ 10.8
				     in eV 27.211 383 86(68) eV 2.5 ~ 10.8
				     quantum of circulation h/2me 3.636 947 5199(50) ~ 10.4 m2 s.1 1.4 ~ 10.9
				     h/me 7.273 895 040(10) ~ 10.4 m2 s.1 1.4 ~ 10.9
				     Electroweak
				     Fermi coupling constantc GF/(Phc)3 1.166 37(1) ~ 10.5 GeV.2 8.6 ~ 10.6
				     weak mixing angled W (on-shell scheme)
				     sin2 W = s2
						W  1 . (mW/mZ)2 sin2 W 0.222 55(56) 2.5 ~ 10.3
						Electron, e.
						electron mass me 9.109 382 15(45) ~ 10.31 kg 5.0 ~ 10.8
						in u, me = Ar(e) u (electron
	relative atomic mass times u) 5.485 799 0943(23) ~ 10.4 u 4.2 ~ 10.10
	energy equivalent mec2 8.187 104 38(41) ~ 10.14 J 5.0 ~ 10.8
	in MeV 0.510 998 910(13) MeV 2.5 ~ 10.8
	electron-muon mass ratio me/mm 4.836 331 71(12) ~ 10.3 2.5 ~ 10.8
	electron-tau mass ratio me/mt 2.875 64(47) ~ 10.4 1.6 ~ 10.4
	electron-proton mass ratio me/mp 5.446 170 2177(24) ~ 10.4 4.3 ~ 10.10
	electron-neutron mass ratio me/mn 5.438 673 4459(33) ~ 10.4 6.0 ~ 10.10
	electron-deuteron mass ratio me/md 2.724 437 1093(12) ~ 10.4 4.3 ~ 10.10
	electron to alpha particle mass ratio me/ma 1.370 933 555 70(58) ~ 10.4 4.2 ~ 10.10
	electron charge to mass quotient .e/me .1.758 820 150(44) ~ 1011 C kg.1 2.5 ~ 10.8
	   electron molar mass NAme M(e),Me 5.485 799 0943(23) ~ 10.7 kg mol.1 4.2 ~ 10.10
	     Compton wavelength h/mec C 2.426 310 2175(33) ~ 10.12 m 1.4 ~ 10.9
	     C/2p = a0 = 2/4pR C 386.159 264 59(53) ~ 10.15 m 1.4 ~ 10.9
			     classical electron radius 2a0 re 2.817 940 2894(58) ~ 10.15 m 2.1 ~ 10.9
			     Thomson cross section (8p/3)r2
			     e e 0.665 245 8558(27) ~ 10.28 m2 4.1 ~ 10.9
			     electron magnetic moment e .928.476 377(23) ~ 10.26 J T.1 2.5 ~ 10.8
			     to Bohr magneton ratio e/B .1.001 159 652 181 11(74) 7.4 ~ 10.13
			     to nuclear magneton ratio e/N .1838.281 970 92(80) 4.3 ~ 10.10
			     electron magnetic moment
			     anomaly |e|/B . 1 ae 1.159 652 181 11(74) ~ 10.3 6.4 ~ 10.10
			     electron g-factor .2(1 + ae) ge .2.002 319 304 3622(15) 7.4 ~ 10.13
			     electron-muon
			     magnetic moment ratio e/m 206.766 9877(52) 2.5 ~ 10.8
			     electron-proton
			     magnetic moment ratio e/p .658.210 6848(54) 8.1 ~ 10.9
			     electron to shielded proton
			     magnetic moment ratio e/ʁ
			     p .658.227 5971(72) 1.1 ~ 10.8
			     (H2O, sphere, 25 .C)
			     
		  

Wind river EVAL-37360

 2
 1.0+0.0i
-1.0+0.0i
 3
 1.0+0.0i 
-0.5+0.866025403784439i -0.5-0.866025403784438i
 4
 1.0 +0.0i
 0.0 +1.0i
-1.0 +0.0i
-0.0 -1.0i
 5
 1.0+0.0i
 0.309016994374947+0.951056516295154i
-0.809016994374947+0.587785252292473i
-0.809016994374948-0.587785252292473i
 0.309016994374947-0.951056516295154i
 6
 1.0+0.0i
 0.5+0.866025403784439i
-0.5+0.866025403784439i
-1.0+0.0i
-0.5-0.866025403784438i
 0.5-0.866025403784439i
 7
 1.0+0.0i
 0.623489801858734+0.78183148246803i
-0.222520933956314+0.974927912181824i
-0.900968867902419+0.433883739117558i
-0.900968867902419-0.433883739117558i
-0.222520933956315-0.974927912181824i
 0.623489801858733-0.78183148246803i
 8
 1.0+0.0i
 0.707106781186548+0.707106781186547i
 0.0+1.0i
-0.707106781186547+0.707106781186548i
-1.0+0.0i
-0.707106781186548-0.707106781186547i
-0.0-1.0i
 0.707106781186547-0.707106781186548i
 9 1.0+0.0i
 0.766044443118978+0.642787609686539i
 0.17364817766693+0.984807753012208i
-0.5+0.866025403784439i
-0.939692620785908+0.342020143325669i
-0.939692620785908-0.342020143325669i
-0.5-0.866025403784438i
 0.17364817766693-0.984807753012208i
 0.766044443118978-0.64278760968654i
10
 1.0+0.0i
 0.809016994374947+0.587785252292473i
 0.309016994374947+0.951056516295154i
-0.309016994374947+0.951056516295154i
-0.809016994374947+0.587785252292473i
-1.0+0.0i
-0.809016994374948-0.587785252292473i
-0.309016994374948-0.951056516295154i
 0.309016994374947-0.951056516295154i
 0.809016994374947-0.587785252292473i


/*
tetrahedron   b4 = pi/2 - a4/2 = 35.26439
    v1 = ( cos(b4), 0, sin(b4))
    v2 = (-cos(b4), 0, sin(b4))
    v3 = ( 0, cos(b4), -sin(b4))
    v4 = ( 0,-cos(b4), -sin(b4))


cube
    faces
    v1 =  0, 0, 1
    v2 =  1, 0, 0
    v3 =  0, 1, 0
    v4 =  0,-1, 0
    v5 = -1, 0, 0
    v6 =  0, 0,-1


octahedron
    faces                       edges
    v1 = ( 1, 1, 1)/3**0.5        e1 = ( 1, 0,1)/2**0.5
    v2 = (-1, 1, 1)/3**0.5        e2 = ( 0, 1,1)/2**0.5
    v3 = (-1,-1, 1)/3**0.5        e3 = (-1, 0,1)/2**0.5
    v4 = ( 1,-1, 1)/3**0.5        e4 = ( 0,-1,1)/2**0.5
    v5 = (-1, 1,-1)/3**0.5
    v6 = ( 1, 1,-1)/3**0.5
    v7   ( 1,-1,-1)/3**0.5
    v8 = (-1,-1,-1)/3**0.5
*/





/*  dodecahedron       5.0*(cos(angle12))**2 = 1.0
                                 angle12 = 63.43494882292
         cos(pi/5) = 0.80901699
         sin(pi/5) = 0.58778525
         sin(0.4 pi) = 0.95105652
         cos(0.4 pi) = 0.30901699
         sin(0.8 pi) = 0.58778525
         cos(0.8 pi) =-0.80901699

icosahedron vertices or dodecahedron faces
unit vectors:
     v1 =  0,0,1
     v2 =  0.89442719, 0, 0.44721360
     v3 =  0.27639320, 0.85065081, 0.44721360
     v4 = -0.72360680, 0.52573111, 0.44721360
     v5 = -0.72360680,-0.52573111, 0.44721360
     v6 =  0.27639320,-0.85065081, 0.44721360

     v7 = -0.27639320, 0.85065081,-0.44721360
     v8 =  0.72360680, 0.52573111,-0.44721360
     v9 =  0.72360680,-0.52573111,-0.44721360
     va = -0.27639320,-0.85065081,-0.44721360
     vb = -0.89442719,-0.0,-0.44721360
     vc =  0,0,-1


icosahedron faces or dodecahedron vertices
     w5 = (v6-v1) x (v2-v1) = 0.47022820, 0.34164078, 0.76084521 
     w1 = (v2-v1) x (v3-v1) = 0.47022820,-0.34164078, 0.76084521
      unit(w5) = 0.49112347, 0.35682208, 0.79465447
      unit(w1) = 0.49112347,-0.35682208, 0.79465447
          angle20 = acos(unit(w1) dot unit(w5)) = acos(.74535597)
          angle20 = (5/9)**0.5
            .729727656227 radians  41.81031489578 degrees

     w2 = (v3-v1) x (v4-v1) = -0.18759247, -0.57735027, 0.79465447
     w3 = (v4-v1) x (v5-v1) = -0.60706200, 0.0, 0.79465447
     w4 = (v5-v1) x (v6-v1) = -0.18759247, 0.57735027, 0.79465447

                                   accurate to 7 decimal places:
     w6 =  2  9 8   0.982 24695  0.0          -0.187 59247 
      7    8  3 2   0.794 65448  0.577 35027   0.187 59247
      8    3  8 7   0.303 53100  0.934 17236  -0.187 59247
      9    7  4 3  -0.303 53100  0.934 17236   0.187 59247
      10   4  7 b  -0.794 65448  0.577 35027  -0.187 59247
     w11   b  5 4  -0.982 24695  0.0           0.187 59247
      12   5  b a  -0.794 65448  -0.577 35027  -0.187 59247
      13   a  6 5  -0.303 53100  -0.934 17236   0.187 59247
      14   6  a 9   0.303 53100  -0.934 17236  -0.187 59247
      15   9  2 6   0.794 65448  -0.577 35027   0.187 59247


     w16= -0.49112347, -0.35682208, -0.79465447   
     w17=  0.18759247, -0.57735027,-0.79465447   
      16 =  0.60706200, 0.0, -0.79465447
      18 =  0.18759247,  0.57735027,-0.79465447
      20 = -0.49112347, 0.35682208,-0.79465447

  icosohedron edges  b20 = a12/2 = 31.71747441146
                     cos(b20) =
                     sin(b20) =
     e1 = (cos(b20),0,sin(b20))       .850650808,0,.5257311121
     e2 = (cos(b20)cos(0.4pi),cos(b20)sin(0.4pi),sin(b20))
     e3 = (-cos(b20)cos(0.2pi),cos(b20)sin(0.2pi),sin(b20))
     e4 = (-cos(b20)cos(0.2pi),-cos(b20)sin(0.2pi),sin(b20)
     e5 = (cos(b20)cos(0.4pi),-cos(b20)sin(0.4pi),sin(b20)

        -unit(e3+e4) dot e1
         unit(cos(b20)cos(0.2pi),0,sin(b20)) dot  (cos(b20),0,sin(b20))
          .79465447,0,-.607061998         37.3773682


  dodecahedron edges b12 = a20/2 =
     e1 = (cos(b12),0,sin(b12))
     e2 = (-0.5*cos(b12),0.866*cos(b12),sin(b12))
     e3 = (-0.5*cos(b12),-0.866*cos(b12),sin(b12))

*/

/*
http://www.dnaco.net/~michael/domes/books/mathematics.html  geodesic@dnaco.net
   Michael Rader


http://www.povray.org/rtn/rtnv4n1.html#art28

 (0,+-p,+-1), (+-1,0,+-p), (+-p,+-1,0)
 (0,+-i,+-p), (+-p,0,+-i), (+-i,+-p,0), (+-1,+-1,+-1)
 p= (sqrt(5)+1)/2 i= (sqrt(5)-1)/2 = 1/9 = p-1

HSM Coxeter 1948 Regular Polytopes p 52-53 Methuen London

http://www.faqs.org/faqs/graphics/algorithms-faq/  6.07
  http://cm.bell-labs.com/netlib/polyhedra/index.html
  http://netlib.bell-labs.com/netlib/polyhedra/index.html
  http://www.netlib.org/polyhedra/index.html
 http://www.cc.iastate.edu/old_answers/packages/graphics/algos.faq.html
 http://www2.hku.nl/~lennart1/docs/algos.txt
 http://www.chesworth.com/pv/graphics/graphics_algorithms_faq.htm
 http://www.scidiv.bcc.ctc.edu/Math/voroni.html

*/
