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For 0<t<2pi and 0<R<1.5; (for example)
(or in alternative, -pi<t<+pi)
x=R*cos(2*t) * (3 - cos(3*t))
y=R*sin(2*t) * (3 - cos(3*t))
z=R*sin(3*t)

Tfactor = (a + b/polyfoldOrder) * atan2(y,x)
x := sqrt(x^2+y^2)-R1
Rotate(x,z,Tfactor)

Angle = (pi/2 - atan2(x,z)) * polyfoldOrder / twopi
Angle = roundInt(angle)
Angle = Angle / polyfoldOrder * twopi
Rotate(x,z,Angle)
x = x + R3

// we modify copies of the variables not the variables ;)
x = Vec.x; y = Vec.y; z = Vec.z;
// try any + or - integer for a & b. Neg values change the handedness
// If you are greedy use only b and set a = 1. Less user friendly btw
Mobius = (a + b/polyfoldOrder) * atan2(y,x)
x := hypot(x,y)-R1 // from now on we will not use y anymore - act on z-rho section
Rotate(x,z,Mobius)
// now do the magic polyfold. But polyfoldOrder must be integer too! 
// I stole this transform from PolygonalBarnsleym in sam.ufm ! It generates those kaleidoscope things with ease
Angle = (pi/2 - atan2(x,z)) * polyfoldOrder / twopi
Angle = roundInt(angle)
Angle = Angle / polyfoldOrder * twopi
Rotate(x,z,Angle)
x = x - R3
// final steps now ... dun dun dunnn ...
Mag = hypot(x,z) - R2
// Done :D
return Mag;

// Replace hypot() with max() or min() and see what happens ... ;)

// My settings R1 = 2 , R2 = .4 , R3 = .5
// trefoil is of order 2, then a = b = 1 (the simplest knot)

void rotate(inout vec2 v, float angle) {
  v = vec2(cos(angle)*v.x+sin(angle)*v.y,-sin(angle)*v.x+cos(angle)*v.y);
}

float DE(vec3 p) {
	float mobius = (a+b/polyfoldOrder) * atan(p.y,p.x);
	p.x = length(p.xy)-R1;
	rotate(p.xz,mobius);	
	float m = polyfoldOrder/(2.*PI);
	float angle = floor(.5+m*(PI/2.-atan(p.x,p.z)))/m;
	rotate(p.xz,angle);
	p.x =p.x - R3;
	return length(p.xz)-R2;
}

pt3.x = pt4.x-((pt4.w-ppdist)*(pt4.x-obspt.x)/(pt4.w-obspt.w)) 
pt3.y = pt4.y-((pt4.w-ppdist)*(pt4.y-obspt.y)/(pt4.w-obspt.w)) 
pt3.z = pt4.z-((pt4.w-ppdist)*(pt4.z-obspt.z)/(pt4.w-obspt.w)) 

ppdist = the w value of the picture realm.
Make it less than the smallest point on your object (my tesseract's points are 1 or -1 in each directionm, and so I set this value at -2..) 
Then the observation point (mine is set at 0,0,0,-4) 
What these formulas are doing is to find out where a line crosses the picture realm when drawn from a point on the object
 to the observer's position. If you think about it, this is why we see things the way we do.
Everything we see is gathered to a point (our eye). :-) To further reduce it to 2D (for display on a monitor...) 

pt2.x = pt3.x-((pt3.z-ppdist)*(pt3.x-obspt.x)/(pt3.z-obspt.z)) 
pt2.y = pt3.y-((pt3.z-ppdist)*(pt3.y-obspt.y)/(pt3.z-obspt.z)) 

return abs(distMult * Trefoil(p) / DEfactor)

#info tore-imbeddebal knots by knighty (2012). Based on DarkBeam's idea (http://www.fractalforums.com/new-theories-and-research/not-fractal-but-funny-trefoil-knot-routine/30/)
#include "DE-Raytracer.frag"
#group Tore_knots

#define PI 3.14159

//Radius of the tubes
uniform float tubeRadius; slider[0,0.1,0.5]

//Radius of the goup of tubes
uniform float groupRadius; slider[0,0.4,0.5]

//Radius of the whole object (because it looks like a torus (-:)
uniform float objectRadius; slider[0,1,1]

//number of tubes
uniform int    tubesNumber; slider[1,3,10]

//rotation rate of the tubes
uniform int    tubesRotMulN; slider[-20,3,20]

//rotation
uniform float rotationAngle; slider[0,1,360]

uniform float time;

float Ncylinder(vec2 p, int n){
	float a=PI/float(n);
	vec2 nor=vec2(sin(a),-cos(a));
	for(int i=0;i<n/1;i++){
		p.y=abs(p.y);
		float t=-2.*dot(nor,p);	p+=max(0.,t)*nor;
	}
	p.x-=groupRadius;
	return length(p)-tubeRadius;
}
vec3 twist(vec3 p, float ra){
	ra*=p.z;
	float ca=cos(ra),sa=sin(ra);
	return vec3(p.x*ca+p.y*sa,-p.x*sa+p.y*ca,p.z);
}
vec3 bend2PI(vec3 p){
	return vec3(length(p.xz),p.y,atan(p.z,p.x));
}
vec3 rotate(vec3 p){
	float ra= rotationAngle*2.*PI/360.;
	float ca=cos(ra),sa=sin(ra);
	return vec3(p.x*ca+p.y*sa,-p.x*sa+p.y*ca,p.z);
}
float DE(vec3 p) {
	p=bend2PI(p);
	p.x-=objectRadius;
	p=twist(p,float(tubesRotMulN)/float(tubesNumber));//one can compute the fudge factor due to twisting
	p=rotate(p);
	float d=Ncylinder(p.xy, tubesNumber);
	return d;
}
#preset default
FOV = 0.62536
Eye = -0.43734,3.38595,0.179052
Target = 0.681321,-5.38885,-0.350126
Up = 0.913916,0.0926774,0.395181
AntiAlias = 1
Detail = -3
DetailAO = -1.57143
FudgeFactor = 0.80723
MaxRaySteps = 64
BoundingSphere = 4 Locked
Dither = 0 Locked
NormalBackStep = 1
AO = 0,0,0,0.90123
Specular = 4.4304
SpecularExp = 16
SpotLight = 0.435294,0.737255,1,0.5
SpotLightDir = 0.65626,0.5
CamLight = 1,0.941176,0.898039,1.0566
CamLightMin = 0
Glow = 1,1,1,0
GlowMax = 20
Fog = 0
HardShadow = 0
ShadowSoft = 12.9032
Reflection = 0
BaseColor = 0.701961,0.701961,0.701961
OrbitStrength = 0
X = 0.411765,0.6,0.560784,0.41748
Y = 0.666667,0.666667,0.498039,-0.16504
Z = 1,0.258824,0.207843,1
R = 0.0823529,0.278431,1,0.82352
BackgroundColor = 0.607843,0.866667,0.560784
GradientBackground = 0.3261
CycleColors = true
Cycles = 4.04901
EnableFloor = false
FloorNormal = 0,0,0
FloorHeight = 0
FloorColor = 1,1,1
tubesNumber = 5
tubesRotMulN = 6
rotationAngle = 234.547
groupRadius = 0.25904
objectRadius = 0.74074
tubeRadius = 0.07304
#endpreset

#info knot thingy by knighty (2012). Based on an idea by DarkBeam from fractalforums (http://www.fractalforums.com/new-theories-and-research/not-fractal-but-funny-trefoil-knot-routine/30/)
#include "DE-Raytracer.frag"
#group Trefoil

#define PI 3.14159

//Radius of the tubes
uniform float tubeRadius; slider[0,0.1,0.5]

//Radius of the goup of tubes
uniform float groupRadius; slider[0,0.4,0.5]

//Radius of the whole object (because it looks like a torus (-:)
uniform float objectRadius; slider[0,1,1]

//Rotation Numerator X: actually not a rotation. This is frequency in x direction
uniform int    RotNumeratorX; slider[-10,2,10]

//Rotation Numerator Y: actually not a rotation. This is frequency in y direction. (lissajou figure)
uniform int    RotNumeratorY; slider[-10,4,10]

//Rotation Denominator: this is the rotation "speed" in xz plane
uniform int    RotDenominator; slider[1,3,20]

//Rotations number: how many instances to check. related to the period of the knot. Have to find math formula for that. 
uniform int    Rotations; slider[1,1,10]

float Cylinder(vec2 p){
	p.x-=groupRadius;
	return length(p)-tubeRadius;
}

float twist(vec3 p){//seen from above it is a lissajou fugure
	float ra =p.z*float(RotNumeratorX)/float( RotDenominator);
	float raz=p.z*float(RotNumeratorY)/float(RotDenominator);
	return length(p.xy-vec2(groupRadius*cos(ra)+objectRadius,groupRadius*sin(raz)+objectRadius))-tubeRadius;
}

vec3 bend2PI(vec3 p){
	return vec3(length(p.xz),p.y,atan(p.z,p.x));
}

float DE(vec3 p) {
	float r=length(p.xz), ang=atan(p.z,p.x),y=p.y;
	float d=10000.;
	for(int i=0; i<Rotations;i++){
		vec3 p=vec3(r,y,ang+2.*PI*float(i));
		p.x-=objectRadius;
		d=min(d,twist(p));
	}
	return d;
}
#preset default
FOV = 0.62536
Eye = -0.684574,2.97917,-0.56351
Target = 1.28819,-5.52322,0.968231
Up = -0.474302,-0.261493,-0.84063
AntiAlias = 1
Detail = -3
DetailAO = -1.57143
FudgeFactor = 0.66265
MaxRaySteps = 64
BoundingSphere = 4 Locked
Dither = 0 Locked
NormalBackStep = 1
AO = 0,0,0,0.90123
Specular = 4.4304
SpecularExp = 16
SpotLight = 0.435294,0.737255,1,0.5
SpotLightDir = 0.65626,0.5
CamLight = 1,0.941176,0.898039,1.0566
CamLightMin = 0
Glow = 1,1,1,0
GlowMax = 20
Fog = 0
HardShadow = 0
ShadowSoft = 12.9032
Reflection = 0
BaseColor = 0.701961,0.701961,0.701961
OrbitStrength = 0
X = 0.411765,0.6,0.560784,0.41748
Y = 0.666667,0.666667,0.498039,-0.16504
Z = 1,0.258824,0.207843,1
R = 0.0823529,0.278431,1,0.82352
BackgroundColor = 0.607843,0.866667,0.560784
GradientBackground = 0.3261
CycleColors = true
Cycles = 4.04901
EnableFloor = false
FloorNormal = 0,0,0
FloorHeight = 0
FloorColor = 1,1,1
tubeRadius = 0.07534
groupRadius = 0.29851
objectRadius = 0.43077
Rotations = 3
RotDenominator = 3
RotNumeratorX = -2
RotNumeratorY = -4
#endpreset