Cône

ps={Orange,Opacity[0.85],Specularity[1,50],EdgeForm[]};
max=5;
haut=ParametricPlot3D[{r Cos[t],r Sin[t],r},{r,0,max},{t,0,2π},Mesh->False, Boxed->False, Axes-> None, Ticks->None,PlotStyle->ps];
bas=ParametricPlot3D[{r Cos[t],r Sin[t],-r},{r,0,max},{t,0,2π},Mesh->False, Boxed->False, Axes-> None, Ticks->None,PlotStyle->ps];
Show[haut,bas, PlotRange->All]

Show[haut]

Hélicoïde

pt[u_,v_,α_]:={Cos[α] Sinh[v] Sin[u]+Sin[α] Cosh[v] Cos[u],
-Cos[α] Sinh[v] Cos[u]+Sin[α] Cosh[v] Sin[u],
u Cos[α]+ v Sin[α]}

ps={Red,Opacity[0.85],Specularity[1,50]};
minV=-2.5;
maxV=2.5;
vp={2.6,-4.8,1.5};
is=800;

ParametricPlot3D[pt[u,v,0],{u,0,2π},{v,minV, maxV},Mesh->False, Boxed->False, Axes-> None, Ticks->None,PlotStyle->ps,PlotPoints->{50,50},ViewPoint->vp]

Tractrice

a=1;
min=0.2;
ps={Blue,Opacity[0.65],Specularity[1,50]};
haut=ParametricPlot3D[{r Cos[t],r Sin[t],a Log[(a+Sqrt[a^2-r^2])/r]-Sqrt[a^2-r^2]},
{r,min,a},{t,0,2π},Mesh->False, Boxed->False, Axes-> None, Ticks->None,PlotStyle->ps,PlotPoints->{50,50}];
bas=ParametricPlot3D[{r Cos[t],r Sin[t],-(a Log[(a+Sqrt[a^2-r^2])/r]-Sqrt[a^2-r^2])},
{r,min,a},{t,0,2π},Mesh->False, Boxed->False, Axes-> None, Ticks->None,PlotStyle->ps,PlotPoints->{50,50}];
Show[haut,bas,PlotRange->All]

Surface de Scherk

σ[x_,y_]:=Log[Cos[x]/Cos[y]]

a=1;
min=0.2;
ϵ=0.00001;
ps={Green,Opacity[0.85],Specularity[1,50],EdgeForm[]};
delx=0;
dely=0;
pp={30,30};
z00=Plot3D[σ[x,y],{x,-π/2+delx+ϵ,π/2+delx-ϵ},{y,-π/2+dely+ϵ,π/2+dely-ϵ},Mesh->False, Boxed->False, Axes-> None, Ticks->None,PlotStyle->ps,PlotPoints->pp];
delx=π;
dely=π;
z11=Plot3D[σ[x,y],{x,-π/2+delx+ϵ,π/2+delx-ϵ},{y,-π/2+dely+ϵ,π/2+dely-ϵ},Mesh->False, Boxed->False, Axes-> None, Ticks->None,PlotStyle->ps,PlotPoints->pp];
delx=2π;
dely=0;
z20=Plot3D[σ[x,y],{x,-π/2+delx+ϵ,π/2+delx-ϵ},{y,-π/2+dely+ϵ,π/2+dely-ϵ},Mesh->False, Boxed->False, Axes-> None, Ticks->None,PlotStyle->ps,PlotPoints->pp];
delx=0;
dely=2π;
z02=Plot3D[σ[x,y],{x,-π/2+delx+ϵ,π/2+delx-ϵ},{y,-π/2+dely+ϵ,π/2+dely-ϵ},Mesh->False, Boxed->False, Axes-> None, Ticks->None,PlotStyle->ps,PlotPoints->pp];
delx=2π;
dely=2π;
z22=Plot3D[σ[x,y],{x,-π/2+delx+ϵ,π/2+delx-ϵ},{y,-π/2+dely+ϵ,π/2+dely-ϵ},Mesh->False, Boxed->False, Axes-> None, Ticks->None,PlotStyle->ps,PlotPoints->pp];

Show[z00,z11,z02,z20,z22,PlotRange->All]

Surface d'Enneper

enneper[r_,t_]:={(1/6) r (3 Cos[t]-(r^2) Cos[3 t]),-(1/6) r (3 Sin[t]+(r^2) Sin[3 t]),(1/2) (r^2) Cos[2 t]}

tt=2Pi *0.2;
en1=ParametricPlot3D[enneper[r,t],{r,0,2},{t,0,2Pi},PlotRange->All,Mesh->False,Axes->False,PlotPoints->{50,50},Boxed->False,ViewPoint->{5Cos[tt],5Sin[tt],1},PlotStyle->{Specularity[1,15],Opacity[0.8],Red}]

Surface d'Henneberg

σ[u_,v_]:={2*Sinh[u]*Cos[v]-2*Sinh[3u]*Cos[3*v]/3,
2*Sinh[u]*Sin[v]-2*Sinh[3u]*Sin[3v]/3,
2*Cosh[2u]*Cos[2v]}

minU=0.5;
maxU=1;
ParametricPlot3D[σ[u,v],{u,minU,maxU},{v,0, 2π},PlotRange->All,Axes->False,Mesh->False,PlotPoints->{40,60},Boxed->False,PlotStyle->{Specularity[1,15],Opacity[0.8],Blue}]

Une quartique

ContourPlot3D[x^4+y^4+z^4-(x^2+y^2+z^2)^2+3(x^2+y^2+z^2)==3,{x, -2,2}, {y, -2, 2}, {z, -2, 2},Mesh->None,ContourStyle->Directive[Orange,Opacity[0.8],Specularity[White,30]],Axes->None, Ticks->None, Boxed->False]

Cubique de Clebsch

ContourPlot3D[81*(x^3+y^3+z^3)-189*(x^2*y+x^2*z+y^2*x+y^2*z+z^2*x+z^2*y)+54*(x*y*z)+126*(x*y+x*z+y*z)-9*(x^2+y^2+z^2)-9*(x+y+z)+1==0,{x, -1,1}, {y, -1,1}, {z, -1,1},Mesh->None,ContourStyle->Directive[Orange,Opacity[0.8],Specularity[White,30]],Axes->None, Ticks->None, Boxed->False]

Coquille de nautilus

a=.
b=.
c=.
d=.
e=.

a=1.0;
b=1.4;
c=0.05;
d=6.0;
e=-2. ;
minU=-π;
maxU=π;
minV=-2. ;
maxV=25. ;
vv[v_]:=v+(v+e)^2/16
s[v_]:=Exp[-c*vv[v]]
r[u_,v_]:=s[v](a+b Cos[u])
σ[u_,v_]:={r[u,v] Cos[vv[v]],r[u,v] Sin[vv[v]], d(1-s[v]) + s[v]*b*Sin[u]}

ps={Orange,Opacity[0.65],Specularity[1,50],EdgeForm[]};
nautilus=ParametricPlot3D[σ[u,v],{u,minU,maxU},{v,minV, maxV},Mesh->False, Boxed->False, Axes-> None, Ticks->None,PlotStyle->ps,PlotPoints->{40,40},PlotRange->All]

Sites internet vraiment très dangereux :
virtualmathmuseum.org
www.indiana.edu/~minimal/