This worksheet is a part of [url=https://www.geogebra.org/m/jteesrnb][b][color=#0000ff]Nexorade: work doc[/color][/b][/url][b][br][br]Move the Red point.[/b][br][br][b]Setup[/b][br][br]ϕ = (1+sqrt(5))/2[br][br]# 60 elements of Icosahedral symmetry: 60 Rotation matrices[br]#==========================================================[br]Mrz = {{1,(ϕ-1),0}*sqrt((ϕ+1)/(ϕ+2)),{-(ϕ-1),1,0}*sqrt((ϕ+1)/(ϕ+2)),{0,0,1}}[br]LA3 = zip(Invert(Mrz)*{{1,0,0},{0,cos(α),-sin(α)},{0,sin(α),cos(α)}}*Mrz, α,{1,2,3}*72°)[br]LM3 = {{{1,0,0},{0,1,0},{0,0,1}},{{0,0,1},{1,0,0},{0,1,0}},{{0,1,0},{0,0,1},{1,0,0}}}[br]LM30= Join({LM3, Join(Zip(Join(Zip(LM3*A3, A3,LA3))*M3, M3,LM3))})[br]MrO = {{-1,0,0},{0,-1,0},{0,0,-1}}*Invert(LA3(1))*{{1,0,0},{0,-1,0},{0,0,1}}*LA3(1)[br]LM60= Join({LM30,Reverse(LM30 MrO)})[br][br]# Draw spherical icosaeder[br]#========================================[br]arc = CircularArc((0,0,0), (1,0,ϕ)/sqrt(ϕ+2), (0,ϕ,1)/sqrt(ϕ+2) )[br]tri = Zip(ApplyMatrix(M, arc), M, LM3)[br]icosi = Zip(ApplyMatrix(M, arc), M, LM60)[br][br]O = (0, 0, 0)[br]sph = Sphere(O,1)[br]cX = Circle(O,1,xAxis)[br]cY = Circle(O,1,yAxis)[br]cZ = Circle(O,1,zAxis)[br][br]Mi = (1,1,1)/sqrt(3)[br]M3Axis= Line(O,Mi)[br]Ai = (0,ϕ,1)/sqrt(ϕ+2)[br]Bi = (1,0,ϕ)/sqrt(ϕ+2)[br]Ci = (ϕ,1,0)/sqrt(ϕ+2)[br]A5Axis = Line(O,Ai)[br]B5Axis = Line(O,Bi)[br]C5Axis = Line(O,Ci)[br]a2Axis = Line(O,Midpoint(Bi,Ci))[br]b2Axis = Line(O,Midpoint(Ci,Ai))[br]c2Axis = Line(O,Midpoint(Ai,Bi))[br][br]# Draw test point[br]#========================================[br][br]P = PointIn(Sphere(O,1))[br]P60 = Zip(ApplyMatrix(M, P), M, LM60)[br][br]#========================================================[br]# Settings[br]#========================================================[br][br]SetActiveView(-1)[br]SetBackgroundColor("#F0F0F0")[br]ShowAxes(false)[br]ShowGrid(false)[br]CenterView(O)[br][br]SetActiveView(1)[br]ShowAxes(false)[br]ShowGrid(false)[br]CenterView(O)[br][br]#========================================================[br]# Properties[br]#========================================================[br][br]#--- Visibility ---#[br]List={cX,cY,cZ,tri,M3Axis,A5Axis,B5Axis,C5Axis,a2Axis,b2Axis,c2Axis}[br]onSymm = CheckBox("Symmetry",List)[br]SetValue(onSymm,false)[br][br]List={"Mi","Ai","Bi","Ci","arc"}[br]Execute(Zip("SetConditionToShowObject("+obj+",onSymm)", obj,List))[br]onIcosi= CheckBox("Icosi",{icosi})[br][br]List={"O","Ci","cZ","C5Axis","icosi","P","P60"}[br]Execute(Zip("SetVisibleInView("+obj+",1,false)", obj,List))[br][br]#--- Color, Filling and Label ---#[br]SetColor(sph,"White")[br]SetFilling(sph,1)[br][br]Black="Black"[br]List={"O","Mi","M3Axis","arc","tri","icosi","P60"}[br]Execute(Zip("SetColor("+obj+","+Black+")", obj,List))[br]Execute(Zip("ShowLabel("+obj+",false)", obj,List))[br][br]Red="Red"[br]List={"cX","Ai","A5Axis","a2Axis","P"}[br]Execute(Zip("SetColor("+obj+","+Red+")", obj,List))[br]Execute(Zip("ShowLabel("+obj+",false)", obj,List))[br][br]Green="Green"[br]List={"cY","Bi","B5Axis","b2Axis"}[br]Execute(Zip("SetColor("+obj+","+Green+")", obj,List))[br]Execute(Zip("ShowLabel("+obj+",false)", obj,List))[br][br]Blue="Blue"[br]List={"cZ","Ci","C5Axis","c2Axis"}[br]Execute(Zip("SetColor("+obj+","+Blue+")", obj,List))[br]Execute(Zip("ShowLabel("+obj+",false)", obj,List))[br][br]#--- LineThickness ---#[br]List={"cX","cY","cZ","M3Axis","a2Axis","b2Axis","c2Axis","A5Axis","B5Axis","C5Axis"}[br]Execute(Zip("SetLineThickness("+obj+",3)", obj,List))[br]List={"arc","tri","icosi"}[br]Execute(Zip("SetLineThickness("+obj+",2)", obj,List))[br][br]#--- PointSize ---#[br]List={"O","Mi","Ai","Bi","Ci","P60"}[br]Execute(Zip("SetPointSize("+obj+",2)", obj,List))[br][br]List={"Black","Red","Green","Blue","List"}[br]Execute(Zip("Delete("+obj+")", obj,List))