Uploading this worksheet gives following error message:[br][br]Error Opening file failed[br] error in <expression>: label=Bsolve, exp= (((-z(NSx(1))))/pi*180°) [br][br]I used a slightly different calculation than Chris Kitrick.[br]Nsolve provides a quick answer to this relatively simple formula.[br]Nsolve doesn't find solutions for more complicated formulas in larger nexorades.[br][br]ϕ = (1+sqrt(5))/2[br]c = atand(1/ϕ)[br]a_{Bc}(x) = atand(cos(x) tan(c))[br]b_{Bc}(x) = asind(sin(x) sin(c))[br]B36(x) = atand(tan(b_{Bc}(x)/2) / sin(a_{Bc}(x)))[br][br]NSx = NSolve(B36(x) = 36°, x = 0)[br]Bsolve = (-z(NSx(1))) /pi * 180°[br][br]B = 56.93190841766905°[br]a = a_{Bc}(B) / pi * 180°[br]b = b_{Bc}(B) / pi * 180°[br][br]a = 18.635196378034680°[br]b = 26.140549500762827° (two times Kitrick's b.)

[url=https://groups.google.com/g/geodesichelp/c/RFBZ6uFmsjU/m/QfiMqboLBAAJ][b][color=#0000ff]New Nexorade/Rotegrity project[/color][/b][/url] : 15 jan 2019 02:53:13[br][br]Chris Kitrick,[br][br][br]Look at the simplest example in the diagram.[br]There are only two unique spherical triangles (0 and 1).[br]Spherical triangle 0 is a right spherical triangle.[br]Given the symmetry spherical triangle 1 is equilateral.[br]The arcs are greater circle segments composed of three (3) equal sub-arcs.[br]The three arcs form a great circle. Considering the equal division of the arcs[br]the following edge angle relationship is true:[br][br] 0b = x / 2[br][br]Since the right spherical triangle 0 is at the pentagon,[br]the B face angle is always 36 degrees.[br]The sides (a,b,c) of the equilateral spherical triangle 1 is 2x.[br][br] 1a = 1b = 1c = 2x[br] [br]Because the three contiguous arcs form a great circle the following must be true:[br][br] 0A + 0A + 1B = 180[br] [br]Now the only question is what is the value of the edge angle x.[br]By simply iterating the edge angle x and solving the two spherical triangles[br]to solve the 180 degree requirement at the blue vertex you arrive at the value:[br] [br] x 26.14054951 0.45623866[br][br]Here are the final spherical angle values for the two triangles:[br][br]Tri a b c A B C[br]00 18.63519637 13.07027475 22.62775606 56.15355653 36.00000000 90.00000000[br]01 52.28109899 52.28109899 52.28109899 67.69288693 67.69288693 67.69288693[br][br]You'll notice the derived number (0.45623866) differs slightly from Taff's (0.456158).[br]Again this is the simplest case but it gives you the idea. No twisting required.[br][br]NOTE: all numbers are angles in degrees except for 0.45623866 which is the length[br]of the arc segment for unit radius sphere.[br][br] 0.45623866 = ( 26.14054951 / 360.0 ) * 2.0 * 3.141592654[br][br]Cheers, Chris[br]