The Cycloheptane Molecule: c = 1/3

ring rs=0,(v,w,x,y,z,t),dp;
ideal i=
  81y2z2-54wyz+54y2z+54yz2-72w2+198wy-207y2+
   198wz-225yz-207z2+114w-141y-141z+10,
  81w2x2+54w2x+54wx2-54wxz-207w2-225wx-207x2+
   198wz+198xz-72z2-141w-141x+114z+10,
  324vw2x+432vw2+540vwx+432w2x-432wxy-432vwz+324wyz+
   180vw+846w2-576vx+180wx-306wy+144xy+144vz-306wz
   -36yz+12v+585w+12x-318y-318z-79,
  81v2w2+54v2w+54vw2-54vwy-207v2-225vw-207w2+198vy+
   198wy-72y2-141v-141w+114y+10;

The equations describe a curve R⁵. The projection to the w,x - plane is computed as follows: ideal j=homog(i,t);
intvec hi=1,0,0,0,-4,0,0,0,6,2,-3,0,-3,-2,3,0;
ideal k3=eliminate(j,vyz,hi);
k3=subst(k3,t,1);
size(k3[1]);

==>

357

Result:	K3;	Equation of the projection to the w,x - plane
	LIB "surf.lib"; plot(K3[1]);	Image of the curve K3=0 in the w,x - plane