Starting from a circle, here are all possible ways to bisecting rotate and nonintersecting sweep a toratope into n+1 dimensions. The implicit definition is shown with a fiber bundle sequence and toratopic notation, which defines the equation. By squeezing all of the (),√,+,,²,R,x,y,z math symbols out, we get an abstract representation of the diameter structure. And, by simplifying a complex mathematical idea into an easy to read format, we can peer into deeper truths of the geometry. In studying the unique differences between the hypertoric rings, we only care about four things:
1. How many dimensions?
2. How many diameters?
3. How are the dimensions distributed among the diameters?
4. What is the combinatoric nesting of the diameters?
In this case, dimensions are defined by a capitol ‘I’ , and diameters are defined by a pair of parentheses ‘()’, with at least two dimensions inside ‘(II)’. The nspheres have all available dimensions contained within just one diameter, and take on the form (II), (III), (IIII), (IIIII), etc. Nested diameters (one inside the other), ‘((II)I)’ defines toroidal shapes, the donut ringlike objects with one or more holes. More nested circles means more diameters, and more holes: ((II)I) , ((II)(II)) , (((II)I)(II)) , (((II)I)(II)I)), etc.
Toratopic notation follows the discrete combinatoric integer sequence A000669, rooted trees with nested leaves. Number of possible shapes per dimension is:
1D  1
2D  1
3D  2
4D  5
5D  12
6D  33
7D  90
8D  261
9D  766
10D  2312
How to rotate into N+1

In notation form, for a circle with a dimension marked as ‘x’ : (xI), replace x with,
• Bisecting Rotate : x = II
 (xI) > (III)
• NonIntersecting Sweep : x = (II)
 (xI) > ((II)I)
In mathematical form, for a circle defined as x²+y²  r², replace x² or y² with,
• Bisecting Rotate Around x : y² = y²+z²
 x²+y² r² > x²+y²+z² r²
• NonIntersecting Sweep Around y : x² = (√(x²+z²)R)²
 x²+y² r² > (√(x²+z²)R)² +y² r²
Terms of the Fiber Bundles:

Sn = nsphere
Tn = ntorus
Cn = Clifford flat ntorus, Tn embedded into R^{2n}
 • C2=[S1*S1] = T2 embedded in R^{4}
• C3=[S1*S1*S1 = T3 embedded in R^{6}
• C4=[S1*S1*S1*S1] = T4 embedded in R^{8}
• C5=[S1*S1*S1*S1]*S1 = T5 embedded in R^{10}
[Sm*Sn] = Clifford flat (m+n)manifold, made by embedding SmxSn or SnxSm into R^{(m+n+2)}
 • [S2*S1] = S2xS1 or S1xS2 embedded in R^{5}
• [S2*S2] = S2xS2 embedded in R^{6}
• [S3*S1] = S3xS1 or S1xS3 embedded in R^{6}
• [S3*S2] = S3xS2 or S2xS3 embedded in R^{7}
[(SmxSn)*Sk] = Clifford flat (m+n+k)manifold, made by surface product of SmxSn and Sk (helps define some surfaces)
1 Compact 1manifold in R^{2} ; xy
Degree2 surface of genus0

(II)  S1 : x²+y² = r²
2 Compact 2manifolds in R^{3} ; xyz
Degree2 surface of genus0

(III)  S2 : x²+y²+z² = r²
Degree4 of genus1

((II)I)  T2 : (√(x²+y²)R)² +z² = r²
5 Compact 3manifolds in R^{4} ; xyzw
Degree2 surface of genus0

(IIII)  S3 : x²+y²+z²+w² = r²
Degree4 of genus1

((II)II)  S2xS1 : (√(x²+y²)R)² +z²+w² = r²
((III)I)  S1xS2 : (√(x²+y²+z²)R)² +w² = r²
Degree8 of genus2

((II)(II))  S1xC2 : (√(x²+y²)R1a)² + (√(z²+w²)R1b)² = Rmin²
(((II)I)I)  T3 : (√((√(x²+y²)R1)² +z²)R2)² +w² = Rmin²
12 Compact 4manifolds in R^{5} ; xyzwv
Degree2 surface of genus0

(IIIII)  S4 : x²+y²+z²+w²+v² = r²
Degree4 of genus1

((II)III)  S3xS1 : (√(x²+y²)R)² +z²+w²+v² = r²
((III)II)  S2xS2 : (√(x²+y²+z²)R)² +w²+v² = r²
((IIII)I)  S1xS3 : (√(x²+y²+z²+w²)R)² +v² = r²
Degree8 of genus2

(((II)I)II)  S2xT2 : (√((√(x²+y²)R1)² +z²)R2)² +w²+v² = Rmin²
(((II)II)I)  S1xS2xS1 : (√((√(x²+y²)R1)² +z²+w²)R2)² +v² = Rmin²
(((III)I)I)  T2xS2 : (√((√(x²+y²+z²)R1)² +w²)R2)² +v² = Rmin²

((II)(II)I)  S2xC2 : (√(x²+y²)R1a)² + (√(z²+w²)R1b)² +v² = Rmin²
((III)(II))  S1x[S2*S1] : (√(x²+y²+z²)R1a)² + (√(w²+v²)R1b)² = Rmin²
Degree16 of genus3

(((II)I)(II))  S1xC2xS1 : (√((√(x²+y²)R1a)²+z²)R2)² + (√(w²+v²)R1b)² = Rmin²
(((II)(II))I)  T2xC2 : (√((√(x²+y²)R1a)² + (√(z²+w²)R1b)²)R2)² +v² = Rmin²
((((II)I)I)I)  T4 : (√((√((√(x²+y²)R1)² +z²)R2)² +w²)R3)² +v² = Rmin²
33 Compact 5manifolds in R^{6} ; xyzwvu
Degree2 surface of genus0

(IIIIII)  S5 : x²+y²+z²+w²+v²+u² = r²
Degree4 of genus1

((II)IIII)  S4xS1 : (√(x²+y²)R)² +z²+w²+v²+u² = r²
((III)III)  S3xS2 : (√(x²+y²+z²)R)² +w²+v²+u² = r²
((IIII)II)  S2xS3 : (√(x²+y²+z²+w²)R)² +v²+u² = r²
((IIIII)I)  S1xS4 : (√(x²+y²+z²+w²+v²)R)² +u² = r²
Degree8 of genus2

(((II)I)III)  S3xT2 : (√((√(x²+y²)R1)² +z²)R2)² +w²+v²+u² = Rmin²
(((II)III)I)  S1xS3xS1 : (√((√(x²+y²)R1)² +z²+w²+v²)R2)² +u² = Rmin²
(((IIII)I)I)  T2xS3 : (√((√(x²+y²+z²+w²)R1)² +v²)R2)² +u² = Rmin²

(((II)II)II)  S2xS2xS1 : (√((√(x²+y²)R1)² +z²+w²)R2)² +v²+u² = Rmin²
(((III)I)II)  S2xS1xS2 : (√((√(x²+y²+z²)R1)² +w²)R2)² +v²+u² = Rmin²
(((III)II)I)  S1xS2xS2 : (√((√(x²+y²+z²)R1)² +w²+v²)R2)² +u² = Rmin²

((II)(II)II)  S3xC2 : (√(x²+y²)R1a)² + (√(z²+w²)R1b)² +v²+u² = Rmin²
((III)(II)I)  S2x[S2*S1] : (√(x²+y²+z²)R1a)² + (√(w²+v²)R1b)² +u² = Rmin²
((III)(III))  S1x[S2*S2] : (√(x²+y²+z²)R1a)² + (√(w²+v²+u²)R1b)² = Rmin²
((IIII)(II))  S1x[S3*S1] : (√(x²+y²z²+w²)R1a)² + (√(v²+u²)R1b)² = Rmin²
Degree16 of genus3

((((II)I)I)II)  S2xT3 : (√((√((√(x²+y²)R1)² +z²)R2)² +w²)R3)² +v²+u² = Rmin²
((((II)I)II)I)  S1xS2xT2 : (√((√((√(x²+y²)R1)² +z²)R2)² +w²+v²)R3)² +u² = Rmin²
((((II)II)I)I)  T2xS2xS1 : (√((√((√(x²+y²)R1)² +z²+w²)R2)² +v²)R3)² +u² = Rmin²
((((III)I)I)I)  T3xS2 : (√((√((√(x²+y²+z²)R1)² +w²)R2)² +v²)R3)² +u² = Rmin²

((II)(II)(II))  S2xC3 : (√(x²+y²)R1a)² + (√(z²+w²)R1b)² + (√(v²+u²)R1c)² = Rmin²
(((II)I)(II)I)  S2xC2xS1 : (√((√(x²+y²)R1a)²+z²)R2)² + (√(w²+v²)R1b)² +u² = Rmin²
(((II)(II)I)I)  S1xS2xC2 : (√((√(x²+y²)R1a)² + (√(z²+w²)R1b)² +v²)R2)² +u² = Rmin²
(((II)(II))II)  S2xS1xC2 : (√((√(x²+y²)R1a)² + (√(z²+w²)R1b)²)R2)² +v²+u² = Rmin²
(((III)(II))I)  T2x[S2*S1] : (√((√(x²+y²+z²)R1a)² + (√(w²+v²)R1b)²)R2)² +u² = Rmin²

(((II)I)(III))  S1x[T2*S2] : (√((√(x²+y²)R1a)²+z²)R2)² + (√(w²+v²+u²)R1b)² = Rmin²
(((II)II)(II))  S1x[S2*S1]xS1 : (√((√(x²+y²)R1a)²+z²+w²)R2)² + (√(v²+u²)R1b)² = Rmin²
(((III)I)(II))  S1xC2xS2 : (√((√(x²+y²+z²)R1a)²+w²)R2)² + (√(v²+u²)R1b)² = Rmin²
Degree32 of genus4

(((II)(II))(II))  T2xC3 : (√((√(x²+y²)R1a)² + (√(z²+w²)R1b)²)R2)² + (√(v²+u²)R1c)² = Rmin²
(((II)I)((II)I))  S1xC2xC2 : (√((√(x²+y²)R1a)²+z²)R2a)² + (√((√(w²+v²)R1b)²+u²)R2b)² = Rmin²

((((II)I)I)(II))  S1xC2xT2 : (√((√((√(x²+y²)R1a)²+z²)R2)²+w²)R3)² + (√(v²+u²)R1b)² = Rmin²
((((II)I)(II))I)  T2xC2xS1 : (√((√((√(x²+y²)R1a)²+z²)R2)² + (√(w²+v²)R1b)²)R3)² +u² = Rmin²
((((II)(II))I)I)  T3xC2 : (√((√((√(x²+y²)R1a)² + (√(z²+w²)R1b)²)R2)² +v²)R3)² +u² = Rmin²
(((((II)I)I)I)I)  T5 : (√((√((√((√(x²+y²)R1)² +z²)R2)² +w²)R3)² +v²)R4)² +u² = Rmin²
90 Compact 6manifolds in R^{7} ; xyzwvut
Degree2 surface of genus0

(IIIIIII)  S6 : x²+y²+z²+w²+v²+u²+t² = r²
Degree4 of genus1

((II)IIIII)  S5xS1 : (√(x²+y²)R)² +z²+w²+v²+u²+t² = r²
((III)IIII)  S4xS2 : (√(x²+y²+z²)R)² +w²+v²+u²+t² = r²
((IIII)III)  S3xS3 : (√(x²+y²+z²+w²)R)² +v²+u²+t² = r²
((IIIII)II)  S2xS4 : (√(x²+y²+z²+w²+v²)R)² +u²+t² = r²
((IIIIII)I)  S1xS5 : (√(x²+y²+z²+w²+v²+u²)R)² +t² = r²
Degree8 of genus2

(((II)I)IIII)  S4xS1xS1 : (√((√(x²+y²)R1)² +z²)R2)² +w²+v²+u²+t² = Rmin²
(((II)II)III)  S3xS2xS1 : (√((√(x²+y²)R1)² +z²+w²)R2)² +v²+u²+t² = Rmin²
(((II)III)II)  S2xS3xS1 : (√((√(x²+y²)R1)² +z²+w²+v²)R2)² +u²+t² = Rmin²
(((II)IIII)I)  S1xS4xS1 : (√((√(x²+y²)R1)² +z²+w²+v²+u²)R2)² +t² = Rmin²
(((III)III)I)  S1xS3xS2 : (√((√(x²+y²+z²)R1)² +w²+v²+u²)R2)² +t² = Rmin²
(((IIII)II)I)  S1xS2xS3 : (√((√(x²+y²+z²+w²)R1)² +v²+u²)R2)² +t² = Rmin²
(((IIIII)I)I)  S1xS1xS4 : (√((√(x²+y²+z²+w²+v²)R1)² +u²)R2)² +t² = Rmin²

(((III)I)III)  S3xS1xS2 : (√((√(x²+y²+z²)R1)² +w²)R2)² +v²+u²+t² = Rmin²
(((III)II)II)  S2xS2xS2 : (√((√(x²+y²+z²)R1)² +w²+v²)R2)² +u²+t² = Rmin²
(((IIII)I)II)  S2xS1xS3 : (√((√(x²+y²+z²+w²)R1)² +v²)R2)² +u²+t² = Rmin²

((II)(II)III)  S4x[S1*S1] : (√(x²+y²)R1a)² + (√(z²+w²)R1b)² +v²+u²+t² = Rmin²
((III)(II)II)  S3x[S2*S1] : (√(x²+y²+z²)R1a)² + (√(w²+v²)R1b)² +u²+t² = Rmin²
((III)(III)I)  S2x[S2*S2] : (√(x²+y²+z²)R1a)² + (√(w²+v²+u²)R1b)² +t² = Rmin²
((IIII)(II)I)  S2x[S3*S1] : (√(x²+y²+z²+w²)R1a)² + (√(v²+u²)R1b)² +t² = Rmin²
((IIII)(III))  S1x[S3*S2] : (√(x²+y²+z²+w²)R1a)² + (√(v²+u²+t²)R1b)² = Rmin²
((IIIII)(II))  S1x[S4*S1] : (√(x²+y²+z²+w²+v²)R1a)² + (√(u²+t²)R1b)² = Rmin²
Degree16 of genus3

((((II)I)I)III)  S3xT3 : (√((√((√(x²+y²)R1)² +z²)R2)² +w²)R3)² +v²+u²+t² = Rmin²
((((II)I)III)I)  S1xS3xT2 : (√((√((√(x²+y²)R1)² +z²)R2)² +w²+v²+u²)R3)² +t² = Rmin²
((((II)III)I)I)  T2xS3xS1 : (√((√((√(x²+y²)R1)² +z²+w²+v²)R2)² +u²)R3)² +t² = Rmin²
((((IIII)I)I)I)  T3xS3 : (√((√((√(x²+y²+z²+w²)R1)² +v²)R2)² +u²)R3)² +t² = Rmin²

((((II)II)II)I)  S1xS2xS2xS1 : (√((√((√(x²+y²)R1)² +z²+w²)R2)² +v²+u²)R3)² +t² = Rmin²
((((II)II)I)II)  S2xS1xS2xS1 : (√((√((√(x²+y²)R1)² +z²+w²)R2)² +v²)R3)² +u²+t² = Rmin²
((((II)I)II)II)  S2xS2xT2 : (√((√((√(x²+y²)R1)² +z²)R2)² +w²+v²)R3)² +u²+t² = Rmin²

((((III)I)I)II)  S2xT2xS2 : (√((√((√(x²+y²+z²)R1)² +w²)R2)² +v²)R3)² +u²+t² = Rmin²
((((III)I)II)I)  S1xS2xS1xS2 : (√((√((√(x²+y²+z²)R1)² +w²)R2)² +v²+u²)R3)² +t² = Rmin²
((((III)II)I)I)  T2xS2xS2 : (√((√((√(x²+y²+z²)R1)² +w²+v²)R2)² +u²)R3)² +t² = Rmin²

((II)(II)(II)I)  S3xC3 : (√(x²+y²)R1a)² + (√(z²+w²)R1b)² + (√(v²+u²)R1c)² +t² = Rmin²
((III)(II)(II))  S2x[S2*S1*S1] : (√(x²+y²+z²)R1a)² + (√(w²+v²)R1b)² + (√(u²+t²)R1c)² = Rmin²

(((II)I)(II)II)  S3xC2xS1 : (√((√(x²+y²)R1a)²+z²)R2)² + (√(w²+v²)R1b)² +u²+t² = Rmin²
(((II)I)(III)I)  S2x[T2*S2] : (√((√(x²+y²)R1a)²+z²)R2)² + (√(w²+v²+u²)R1b)² +t² = Rmin²
(((II)II)(II)I)  S2x[S2*S1]xS1 : (√((√(x²+y²)R1a)²+z²+w²)R2)² + (√(v²+u²)R1b)² +t² = Rmin²
(((III)I)(II)I)  S2xC2xS2 : (√((√(x²+y²+z²)R1a)²+w²)R2)² + (√(v²+u²)R1b)² +t² = Rmin²

(((III)I)(III))  S1x[(S1xS2)*S2] : (√((√(x²+y²+z²)R1a)²+w²)R2)² + (√(v²+u²+t²)R1b)² = Rmin²
(((III)II)(II))  S1x[S2*S1]xS2 : (√((√(x²+y²+z²)R1a)²+w²+v²)R2)² + (√(u²+t²)R1b)² = Rmin²
(((IIII)I)(II))  S1xC2xS3 : (√((√(x²+y²+z²+w²)R1a)²+v²)R2)² + (√(u²+t²)R1b)² = Rmin²

(((II)I)(IIII))  S1x[T2*S3] : (√((√(x²+y²)R1a)²+z²)R2)² + (√(w²+v²+u²+t²)R1b)² = Rmin²
(((II)II)(III))  S1x[S2*S2]xS1 : (√((√(x²+y²)R1a)²+z²+w²)R2)² + (√(v²+u²+t²)R1b)² = Rmin²
(((II)III)(II))  S1x[S3*S1]xS1 : (√((√(x²+y²)R1a)²+z²+w²+v²)R2)² + (√(u²+t²)R1b)² = Rmin²

(((II)(II))III)  S3xS1xC2 : (√((√(x²+y²)R1a)² + (√(z²+w²)R1b)²)R2)² +v²+u²+t² = Rmin²
(((III)(II))II)  S2xS1x[S2*S1] : (√((√(x²+y²+z²)R1a)² + (√(w²+v²)R1b)²)R2)² +u²+t² = Rmin²
(((III)(III))I)  T2x[S2*S2] : (√((√(x²+y²+z²)R1a)² + (√(w²+v²+u²)R1b)²)R2)² +t² = Rmin²
(((IIII)(II))I)  T2x[S3*S1] : (√((√(x²+y²+z²+w²)R1a)² + (√(v²+u²)R1b)²)R2)² +t² = Rmin²

(((II)(II)I)II)  S2xS2xC2 : (√((√(x²+y²)R1a)² + (√(z²+w²)R1b)² +v²)R2)² +u²+t² = Rmin²
(((II)(II)II)I)  S1xS3xC2 : (√((√(x²+y²)R1a)² + (√(z²+w²)R1b)² +v²+u²)R2)² +t² = Rmin²
(((III)(II)I)I)  S1xS2x[S2*S1] : (√((√(x²+y²+z²)R1a)² + (√(w²+v²)R1b)² +u²)R2)² +t² = Rmin²
Degree32 of genus4

(((((II)I)I)I)II)  S2xT4 : (√((√((√((√(x²+y²)R1)² +z²)R2)² +w²)R3)² +v²)R4)² +u²+t² = Rmin²
(((((II)I)I)II)I)  S1xS2xT3 : (√((√((√((√(x²+y²)R1)² +z²)R2)² +w²)R3)² +v²+u²)R4)² +t² = Rmin²
(((((II)I)II)I)I)  T2xS2xT2 : (√((√((√((√(x²+y²)R1)² +z²)R2)² +w²+v²)R3)² +u²)R4)² +t² = Rmin²
(((((II)II)I)I)I)  T3xS2xS1 : (√((√((√((√(x²+y²)R1)² +z²+w²)R2)² +v²)R3)² +u²)R4)² +t² = Rmin²
(((((III)I)I)I)I)  T4xS2 : (√((√((√((√(x²+y²+z²)R1)² +w²)R2)² +v²)R3)² +u²)R4)² +t² = Rmin²

(((II)(II))(II)I)  S2xS1xC3 : (√((√(x²+y²)R1a)² + (√(z²+w²)R1b)²)R2)² + (√(v²+u²)R1c)² +t² = Rmin²
(((II)(II))(III))  S1x[(S1xC2)*S2] : (√((√(x²+y²)R1a)² + (√(z²+w²)R1b)²)R2)² + (√(v²+u²+t²)R1c)² = Rmin²
(((II)(II)I)(II))  S1x[(S2xC2)*S1] : (√((√(x²+y²)R1a)² + (√(z²+w²)R1b)² +v²)R2)² + (√(u²+t²)R1c)² = Rmin²
(((III)(II))(II))  T2x[S2*S1*S1] : (√((√(x²+y²+z²)R1a)² + (√(w²+v²)R1b)²)R2)² + (√(u²+t²)R1c)² = Rmin²

(((II)I)((II)I)I)  S2xC2xC2 : (√((√(x²+y²)R1a)²+z²)R2a)² + (√((√(w²+v²)R1b)²+u²)R2b)² +t² = Rmin²
(((II)II)((II)I))  S1x[S2*S1]xC2 : (√((√(x²+y²)R1a)²+z²+w²)R2a)² + (√((√(v²+u²)R1b)²+t²)R2b)² = Rmin²
(((III)I)((II)I))  S1xC2x[S2*S1] : (√((√(x²+y²+z²)R1a)²+w²)R2a)² + (√((√(v²+u²)R1b)²+t²)R2b)² = Rmin²

((((II)I)I)(II)I)  S2xC2xT2 : (√((√((√(x²+y²)R1a)²+z²)R2)²+w²)R3)² + (√(v²+u²)R1b)² +t² = Rmin²
((((II)I)I)(III))  S1x[T3*S2] : (√((√((√(x²+y²)R1a)²+z²)R2)²+w²)R3)² + (√(v²+u²+t²)R1b)² = Rmin²
((((II)I)II)(II))  S1x[S2*S1]xT2 : (√((√((√(x²+y²)R1a)²+z²)R2)²+w²+v²)R3)² + (√(u²+t²)R1b)² = Rmin²
((((II)II)I)(II))  S1xC2xS2xS1 : (√((√((√(x²+y²)R1a)²+z²+w²)R2)²+v²)R3)² + (√(u²+t²)R1b)² = Rmin²
((((III)I)I)(II))  S1xC2xS1xS2 : (√((√((√(x²+y²+z²)R1a)²+w²)R2)²+v²)R3)² + (√(u²+t²)R1b)² = Rmin²

((((II)(II))I)II)  S2xT2xC2 : (√((√((√(x²+y²)R1a)² + (√(z²+w²)R1b)²)R2)² +v²)R3)² +u²+t² = Rmin²
((((II)(II))II)I)  S1xS2xS1xC2 : (√((√((√(x²+y²)R1a)² + (√(z²+w²)R1b)²)R2)² +v²+u²)R3)² +t² = Rmin²
((((II)(II)I)I)I)  T2xS2xC2 : (√((√((√(x²+y²)R1a)² + (√(z²+w²)R1b)² +v²)R2)² +u²)R3)² +t² = Rmin²
((((III)(II))I)I)  T3x[S2*S1] : (√((√((√(x²+y²+z²)R1a)² + (√(w²+v²)R1b)²)R2)² +u²)R3)² +t² = Rmin²

((((II)I)(II))II)  S2xS1xC2xS1 : (√((√((√(x²+y²)R1a)²+z²)R2)² + (√(w²+v²)R1b)²)R3)² +u²+t² = Rmin²
((((II)I)(II)I)I)  S1xS2xC2xS1 : (√((√((√(x²+y²)R1a)²+z²)R2)² + (√(w²+v²)R1b)² +u²)R3)² +t² = Rmin²
((((II)I)(III))I)  T2x[T2*S2] : (√((√((√(x²+y²)R1a)²+z²)R2)² + (√(w²+v²+u²)R1b)²)R3)² +t² = Rmin²
((((II)II)(II))I)  T2x[S2*S1]xS1 : (√((√((√(x²+y²)R1a)²+z²+w²)R2)² + (√(v²+u²)R1b)²)R3)² +t² = Rmin²
((((III)I)(II))I)  T2xC2xS2 : (√((√((√(x²+y²+z²)R1a)²+w²)R2)² + (√(v²+u²)R1b)²)R3)² +t² = Rmin²

(((II)I)(II)(II))  S2xC3xS1 : (√((√(x²+y²)R1a)²+z²)R2)² + (√(w²+v²)R1b)² + (√(u²+t²)R1c)² = Rmin²
(((II)(II)(II))I)  S1xS2xC3 : (√((√(x²+y²)R1a)² + (√(z²+w²)R1b)² + (√(v²+u²)R1c)²)R2)² +t² = Rmin²
Degree64 of genus5

((((II)(II))(II))I)  T3xC3 : (√((√((√(x²+y²)R1a)² + (√(z²+w²)R1b)²)R2)² + (√(v²+u²)R1c)²)R3)² +t² = Rmin²
(((II)(II))((II)I))  S1xC2xC3 : (√((√(x²+y²)R1a)² + (√(z²+w²)R1b)²)R3)² + (√((√(v²+u²)R1c)²+t²)R2)² = Rmin²
((((II)(II))I)(II))  S1xC2xS1xC2 : (√((√((√(x²+y²)R1a)² + (√(z²+w²)R1b)²)R2)² +v²)R3)² + (√(u²+t²)R1c)² = Rmin²
((((II)I)(II))(II))  T2xC3xS1 : (√((√((√(x²+y²)R1a)²+z²)R2)² + (√(w²+v²)R1b)²)R3)² + (√(u²+t²)R1c)² = Rmin²

((((II)I)((II)I))I)  T2xC2xC2 : (√((√((√(x²+y²)R1a)²+z²)R2a)² + (√((√(w²+v²)R1b)²+u²)R2b)²)R3)² +t² = Rmin²
((((II)I)I)((II)I))  S1xC2xC2xS1 : (√((√((√(x²+y²)R1a)²+z²)R2a)²+w²)R3)² + (√((√(v²+u²)R1b)²+t²)R2b)² = Rmin²

(((((II)I)I)I)(II))  S1xC2xT3 : (√((√((√((√(x²+y²)R1a)²+z²)R2)²+w²)R3)²+v²)R4)² + (√(u²+t²)R1b)² = Rmin²
(((((II)I)I)(II))I)  T2xC2xT2 : (√((√((√((√(x²+y²)R1a)²+z²)R2)²+w²)R3)² + (√(v²+u²)R1b)²)R4)² +t² = Rmin²
(((((II)I)(II))I)I)  T3xC2xS1 : (√((√((√((√(x²+y²)R1a)²+z²)R2)² + (√(w²+v²)R1b)²)R3)² +u²)R4)² +t² = Rmin²
(((((II)(II))I)I)I)  T4xC2 : (√((√((√((√(x²+y²)R1a)² + (√(z²+w²)R1b)²)R2)² +v²)R3)² +u²)R4)² +t² = Rmin²
((((((II)I)I)I)I)I)  T6 : (√((√((√((√((√(x²+y²)R1)² +z²)R2)² +w²)R3)² +v²)R4)² +u²)R5)² +t² = Rmin²