// c.f. maxima/20221009.mc & 20211019-1-5p2-3.cdy
Setwindow([-1,1],[-1,1]);
Setunitlen("5cm");
//to move to default positions, delete points
Putpoint("TH",[-5+72/20,-3.0],[TH.x,-3.0]); // -5 ~ -5+180/20=4
Putpoint("FI",[-5+50/40,-3.5],[FI.x,-3.5]); // -5 ~ -5+360/40=4
//Setangle(72,50); // fixed // view from (sin72cos50,sin72sin50,cos72)
Start3d();
Texparent="";

Addax(0);
Putaxes3d(0);

//Paramplot("xma","[XMAX,t]","t=[YMIN,YMAX]",["dr","Num=50"]);
//Paramplot("xmi","[XMIN,t]","t=[YMIN,YMAX]",["dr","Num=50"]);
//Paramplot("yma","[t,YMAX]","t=[XMIN,XMAX]",["dr","Num=50"]);
//Paramplot("ymi","[t,YMIN]","t=[XMIN,XMAX]",["dr","Num=50"]);

//Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]");

Defvar("g",(sqrt(5)-1)/2);
t43=[-1  ,-1  ,-1  ]/sqrt(3);
t24=[-1  ,-1  , 1  ]/sqrt(3);
t14=[-1  , 1  ,-1  ]/sqrt(3);
t40=[-1  , 1  , 1  ]/sqrt(3);
t04=[ 1  ,-1  ,-1  ]/sqrt(3);
t41=[ 1  ,-1  , 1  ]/sqrt(3);
t42=[ 1  , 1  ,-1  ]/sqrt(3);
t34=[ 1  , 1  , 1  ]/sqrt(3);
t20=[  -g, 0  ,-1-g]/sqrt(3);
t31=[   g, 0  ,-1-g]/sqrt(3);
t02=[   g, 0  , 1+g]/sqrt(3);
t13=[  -g, 0  , 1+g]/sqrt(3);
t01=[-1-g,  -g, 0  ]/sqrt(3);
t32=[-1-g,   g, 0  ]/sqrt(3);
t10=[ 1+g,   g, 0  ]/sqrt(3);
t23=[ 1+g,  -g, 0  ]/sqrt(3);
t12=[ 0  ,-1-g,  -g]/sqrt(3);
t30=[ 0  ,-1-g,   g]/sqrt(3);
t21=[ 0  , 1+g,   g]/sqrt(3);
t03=[ 0  , 1+g,  -g]/sqrt(3);
Defvar("h",sqrt((3+g)^2+(4+3*g)^2));
p12=(t43+t01+t24+t30+t12)*sqrt(3)/h; ip12=p12*5/sqrt(3)/h;
p01=(t43+t20+t14+t32+t01)*sqrt(3)/h; ip01=p01*5/sqrt(3)/h;
p20=(t43+t12+t04+t31+t20)*sqrt(3)/h; ip20=p20*5/sqrt(3)/h;
p32=(t40+t13+t24+t01+t32)*sqrt(3)/h; ip32=p32*5/sqrt(3)/h;
p21=(t40+t32+t14+t03+t21)*sqrt(3)/h; ip21=p21*5/sqrt(3)/h;
p13=(t40+t21+t34+t02+t13)*sqrt(3)/h; ip13=p13*5/sqrt(3)/h;
p02=(t41+t30+t24+t13+t02)*sqrt(3)/h; ip02=p02*5/sqrt(3)/h;
p30=(t41+t23+t04+t12+t30)*sqrt(3)/h; ip30=p30*5/sqrt(3)/h;
p23=(t41+t02+t34+t10+t23)*sqrt(3)/h; ip23=p23*5/sqrt(3)/h;
p31=(t42+t03+t14+t20+t31)*sqrt(3)/h; ip31=p31*5/sqrt(3)/h;
p10=(t42+t31+t04+t23+t10)*sqrt(3)/h; ip10=p10*5/sqrt(3)/h;
p03=(t42+t10+t34+t21+t03)*sqrt(3)/h; ip03=p03*5/sqrt(3)/h;

Ptseg3data();

Spaceline("tt00",[t20,t13],["dr","nodisp"]);
Spaceline("tt01",[t13,t04],["dr","nodisp"]);
Spaceline("tt02",[t04,t32],["dr","nodisp"]);
Spaceline("tt03",[t32,t41],["dr","nodisp"]);
Spaceline("tt04",[t41,t20],["dr","nodisp"]);
Spaceline("tt05",[t12,t03],["dr","nodisp"]);
Spaceline("tt06",[t03,t24],["dr","nodisp"]);
Spaceline("tt07",[t24,t31],["dr","nodisp"]);
Spaceline("tt08",[t31,t40],["dr","nodisp"]);
Spaceline("tt09",[t40,t12],["dr","nodisp"]);
Spaceline("tt10",[t01,t23],["dr","nodisp"]);
Spaceline("tt11",[t23,t14],["dr","nodisp"]);
Spaceline("tt12",[t14,t30],["dr","nodisp"]);
Spaceline("tt13",[t30,t42],["dr","nodisp"]);
Spaceline("tt14",[t42,t01],["dr","nodisp"]);
Spaceline("tt15",[t21,t30],["dr","nodisp"]);
Spaceline("tt16",[t14,t02],["dr","nodisp"]);
Spaceline("tt17",[t02,t43],["dr","nodisp"]);
Spaceline("tt18",[t43,t21],["dr","nodisp"]);
Spaceline("tt19",[t20,t34],["dr","nodisp"]);
Spaceline("tt20",[t34,t01],["dr","nodisp"]);
Spaceline("tt21",[t42,t13],["dr","nodisp"]);
Spaceline("tt22",[t32,t10],["dr","nodisp"]);
Spaceline("tt23",[t10,t24],["dr","nodisp"]);
Spaceline("tt24",[t03,t41],["dr","nodisp"]);
Spaceline("tt25",[t34,t12],["dr","nodisp"]);
Spaceline("tt26",[t40,t23],["dr","nodisp"]);
Spaceline("tt27",[t02,t31],["dr","nodisp"]);
Spaceline("tt28",[t10,t43],["dr","nodisp"]);
Spaceline("tt29",[t21,t04],["dr","nodisp"]);

if(Isangle(), //if TH/FI is selected
,
 Startsurf();
 phd=Concatobj([
[ip32,t32,ip01],[ip01,t20,ip20],[ip20,t04,ip30],[ip30,t41,ip02],[ip02,t13,ip32],
//[t32,ip01,t20,ip20,t04,ip30,t41,ip02,t13,ip32], (p12)
[ip20,t12,ip12],[ip12,t24,ip32],[ip32,t40,ip21],[ip21,t03,ip31],[ip31,t31,ip20],
//[t12,ip12,t24,ip32,t40,ip21,t03,ip31,t31,ip20], (p01)
[ip12,t01,ip01],[ip01,t14,ip31],[ip31,t42,ip10],[ip10,t23,ip30],[ip30,t30,ip12],
//[t01,ip01,t14,ip31,t42,ip10,t23,ip30,t30,ip12], (p20)
[ip01,t43,ip12],[ip12,t30,ip02],[ip02,t02,ip13],[ip13,t21,ip21],[ip21,t14,ip01],
//[t43,ip12,t30,ip02,t02,ip13,t21,ip21,t14,ip01], (p32)
[ip31,t20,ip01],[ip01,t01,ip32],[ip32,t13,ip13],[ip13,t34,ip03],[ip03,t42,ip31],
//[t20,ip01,t01,ip32,t13,ip13,t34,ip03,t42,ip31], (p21)
[ip21,t32,ip32],[ip32,t24,ip02],[ip02,t41,ip23],[ip23,t10,ip03],[ip03,t03,ip21],
//[t32,ip32,t24,ip02,t41,ip23,t10,ip03,t03,ip21], (p13)
[ip32,t01,ip12],[ip12,t12,ip30],[ip30,t23,ip23],[ip23,t34,ip13],[ip13,t40,ip32],
//[t01,ip12,t12,ip30,t23,ip23,t34,ip13,t40,ip32], (p02)
[ip02,t24,ip12],[ip12,t43,ip20],[ip20,t31,ip10],[ip10,t10,ip23],[ip23,t02,ip02],
//[t24,ip12,t43,ip20,t31,ip10,t10,ip23,t02,ip02], (p30)
[ip03,t21,ip13],[ip13,t13,ip02],[ip02,t30,ip30],[ip30,t04,ip10],[ip10,t42,ip03],
//[t21,ip13,t13,ip02,t30,ip30,t04,ip10,t42,ip03], (p23)
[ip20,t43,ip01],[ip01,t32,ip21],[ip21,t21,ip03],[ip03,t10,ip10],[ip10,t04,ip20],
//[t43,ip01,t32,ip21,t21,ip03,t10,ip10,t04,ip20], (p31)
[ip30,t12,ip20],[ip20,t20,ip31],[ip31,t03,ip03],[ip03,t34,ip23],[ip23,t41,ip30],
//[t12,ip20,t20,ip31,t03,ip03,t34,ip23,t41,ip30], (p10)
[ip31,t14,ip21],[ip21,t40,ip13],[ip13,t02,ip23],[ip23,t23,ip10],[ip10,t31,ip31]
//[t14,ip21,t40,ip13,t02,ip23,t23,ip10,t31,ip31]  (p03)
              ]);
 VertexEdgeFace("0",phd);
 Nohiddenbyfaces("0","phf3d0",[],["nodisp"]);
  );
 
Listplotc("c1",[ip32,t32,ip01],["nodisp"]);
Shade(["sgc1"],["Color=[0,1,1,0]"]);
Listplotc("c2",[ip01,t20,ip20],["nodisp"]);
Shade(["sgc2"],["Color=[1,1,0,0]"]);
Listplotc("c3",[ip31,t03,ip03],["nodisp"]);
Shade(["sgc3"],["Color=[1,0,1,0]"]);