Este team de redactores ha pasado horas investigando para darle resolución a tus búsquedas, te regalamos la respuesta así que nuestro objetivo es que te sea de gran ayuda.
Solución:
Este código requiere la biblioteca experimental 3dtools.
documentclass[tikz,border=3mm]standalone
usepackagetikz-3dplot
usetikzlibrarybackgrounds,3dtools,shapes.geometric
tikzsetpics/isocahedron/.style=code=
path foreach Coord [count=X] in
(0.,0.,-0.9510565162951536),
(0.,0.,0.9510565162951536),
(-0.85065080835204,0.,-0.42532540417601994),
(0.85065080835204,0.,0.42532540417601994),
(0.6881909602355868,-0.5,-0.42532540417601994),
(0.6881909602355868,0.5,-0.42532540417601994),
(-0.6881909602355868,-0.5,0.42532540417601994),
(-0.6881909602355868,0.5,0.42532540417601994),
(-0.2628655560595668,-0.8090169943749475,-0.42532540417601994),
(-0.2628655560595668,0.8090169943749475,-0.42532540417601994),
(0.2628655560595668,-0.8090169943749475,0.42532540417601994),
(0.2628655560595668,0.8090169943749475,0.42532540417601994)
Coord coordinate (pX) pgfextraxdefNumVerticesX;
%messagenumber of vertices is NumVertices^^J
% normal of screen
path[overlay] (sin(tdplotmaintheta)*sin(tdplotmainphi),
-1*sin(tdplotmaintheta)*cos(tdplotmainphi),
cos(tdplotmaintheta)) coordinate (n)
(-sqrt(1/6),sqrt(3/6),sqrt(2/6)) coordinate (L);
edeflstPast0
foreach poly in
2,12,8,2,8,7,2,7,11,2,11,4,2,4,12,5,9,1,6,5,1,
10,6,1,3,10,1,9,3,1,12,10,8,8,3,7,7,9,11,11,5,4,4,6,12,
5,11,9,6,4,5,10,12,6,3,8,10,9,7,3
pgfmathtruncatemacroionepoly[0]
pgfmathtruncatemacroitwopoly[1]
pgfmathtruncatemacroithreepoly[2]
path[overlay,3d coordinate=(dA)=(pitwo)-(pione),
3d coordinate=(dB)=(pitwo)-(pithree),
3d coordinate=(nA)=(dA)x(dB)] ;
pgfmathtruncatemacrojtestsign(TD("(nA)o(pione)"))
% make sure that the normal points outwards
ifnumjtest<0
path[overlay,3d coordinate=(nA)=(dB)x(dA)];
fi
% compute projection the normal of the polygon on the normal of screen
pgfmathsetmacromyprojTD("(nA)o(n)")
pgfmathsetmacrolprojTD("(nA)o(L)")
pgfmathtruncatemacroitestsign(myproj)
ifnumitest>-1
draw[thick] [fill=white,fill opacity=0.2]
plot[samples at=poly,variable=x](px) -- cycle;
else
beginscope[on background layer]
draw[gray,ultra thin]
plot[samples at=poly,variable=x](px) -- cycle;
endscope
fi
begindocument
tdplotsetmaincoords7065
begintikzpicture[line cap=round,line join=round,
bullet/.style=circle,fill,inner sep=1.5pt]
pic[tdplot_main_coords,scale=2,rotate=30]isocahedron;
%foreach X in 1,...,NumVertices path (pX) node[above]X;
path (p12) node[above]$D$ --
node[bullet,label=above:$N$](N)
(p2) node[above]$A$
(p7) node[left]$B$ --
node[bullet,label=[xshift=3pt]above:$M$]
(p11) node[below right]$C$;
beginscope[xshift=5cm]
path let p1=($(N)-(0,0)$) in
node[regular polygon,regular polygon sides=6,draw,thick,minimum size=2*y1]
(6gon);
path (6gon.corner 1) node[above] $D$
-- node[bullet,label=above:$N$](N')
(6gon.corner 2) node[above] $A$;
draw[thick] (6gon.corner 3) node[left] $M$
-- node[bullet,label=below right:$O$](O)
(6gon.corner 6)
(O) edge (N');
draw ([xshift=-1em]O.center) |- ([yshift=1em]O.center);
endscope
endtikzpicture
enddocument
El icosaedro es giratorio en 3d.
documentclass[tikz,border=3mm]standalone
usepackagetikz-3dplot
usetikzlibrarybackgrounds,3dtools,shapes.geometric
tikzsetpics/isocahedron/.style=code=
path foreach Coord [count=X] in
(0.,0.,-0.9510565162951536),
(0.,0.,0.9510565162951536),
(-0.85065080835204,0.,-0.42532540417601994),
(0.85065080835204,0.,0.42532540417601994),
(0.6881909602355868,-0.5,-0.42532540417601994),
(0.6881909602355868,0.5,-0.42532540417601994),
(-0.6881909602355868,-0.5,0.42532540417601994),
(-0.6881909602355868,0.5,0.42532540417601994),
(-0.2628655560595668,-0.8090169943749475,-0.42532540417601994),
(-0.2628655560595668,0.8090169943749475,-0.42532540417601994),
(0.2628655560595668,-0.8090169943749475,0.42532540417601994),
(0.2628655560595668,0.8090169943749475,0.42532540417601994)
Coord coordinate (pX) pgfextraxdefNumVerticesX;
%messagenumber of vertices is NumVertices^^J
% normal of screen
path[overlay] (sin(tdplotmaintheta)*sin(tdplotmainphi),
-1*sin(tdplotmaintheta)*cos(tdplotmainphi),
cos(tdplotmaintheta)) coordinate (n)
(-sqrt(1/6),sqrt(3/6),sqrt(2/6)) coordinate (L);
edeflstPast0
foreach poly in
2,12,8,2,8,7,2,7,11,2,11,4,2,4,12,5,9,1,6,5,1,
10,6,1,3,10,1,9,3,1,12,10,8,8,3,7,7,9,11,11,5,4,4,6,12,
5,11,9,6,4,5,10,12,6,3,8,10,9,7,3
pgfmathtruncatemacroionepoly[0]
pgfmathtruncatemacroitwopoly[1]
pgfmathtruncatemacroithreepoly[2]
path[overlay,3d coordinate=(dA)=(pitwo)-(pione),
3d coordinate=(dB)=(pitwo)-(pithree),
3d coordinate=(nA)=(dA)x(dB)] ;
pgfmathtruncatemacrojtestsign(TD("(nA)o(pione)"))
% make sure that the normal points outwards
ifnumjtest<0
path[overlay,3d coordinate=(nA)=(dB)x(dA)];
fi
% compute projection the normal of the polygon on the normal of screen
pgfmathsetmacromyprojTD("(nA)o(n)")
pgfmathsetmacrolprojTD("(nA)o(L)")
pgfmathtruncatemacroitestsign(myproj)
ifnumitest>-1
draw[thick] [fill=white,fill opacity=0.2]
plot[samples at=poly,variable=x](px) -- cycle;
else
beginscope[on background layer]
draw[gray,ultra thin]
plot[samples at=poly,variable=x](px) -- cycle;
endscope
fi
begindocument
foreach XX in 0,10,...,350
begintikzpicture[line cap=round,line join=round,
bullet/.style=circle,fill,inner sep=1.5pt]
path (-3.5,-3.5) rectangle (3.5,3.5);
tdplotsetmaincoords60+20*sin(XX)XX
pic[tdplot_main_coords,scale=3]isocahedron;
endtikzpicture
enddocument
Por favor, vea si cumple con el requisito.
documentclass[a4paper]amsart
usepackagegraphics, tkz-berge
begindocument
beginfigure
begintikzpicture
beginscope[rotate=90]
SetVertexNoLabel % <--- This avoids that default $a_0$, .. $b_0$ labels show up
grIcosahedral[form=1,RA=3,RB=1.5]
% Following two lines assign labels to a-like and b-like nodes
% change it as you prefer
AssignVertexLabela$v_0$, $v_1$, $v_2$, $v_3$, $v_4$, $v_5$;
AssignVertexLabelb$v_6$, $v_7$, $v_8$, $v_9$, $v_10$, $v_11$;
% The remaining code is unchanged
SetUpEdge[color=white,style=double=black,double distance=2pt]
EdgeInGraphLoopa6
EdgeFromOneToSelab01,5
Edges(a2,b1,b3,b5,a4)
Edge(a3)(b3)
Edges(a1,b1,b5,a5)
Edges(a2,b3,a4)
endscope
endtikzpicture
endfigure
enddocument
Gracias a @JLDiaz que ha dado la solución: https://tex.stackexchange.com/a/183075/197451
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