<p> Torus & quaternion normalize </p>

bdd93c1f-c2b6-43c0-81fe-7078471a6ee0 10 3 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Rotate the Quaternion system:

Each col permutes 24 ... not offered.

This part is stand alone. Copy/paste in

new work sheet. 'V' is borrowed.

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n v rotate N v length : p n N mod : p p p 0 ≥ p N + p 0 < NOT accounted cases : Ω v : p 0 ≡ i 1 p range Ω i N + p - el v i el : for i p 1 + (N range Ω i p - el v i el : for 21 line cases Ω 51 line :

n 1 :

V 0.267 0.267 - 0.535 0.535 - 0.802 0.802 - 0.267 0.267 42 mat :

q n V 2 col rotate : 0.535 - 0.802 - 0.267 0.267 - 41 mat

<p> Torus & quaternion normalize </p>

5. Define the "UnitV", apply to 'q' q q q norme / : 0.5167 - 0.7746 - 0.2579 0.2579 - 41 mat

6. The rotation 'quat' converter quat 12 q 3 el (2^* - 2 q 4 el (2^* - 2 q 2 el * q 3 el * 2 q 1 el * q 4 el * - 2 q 1 el * q 3 el * 2 q 2 el * q 4 el * + 2 q 1 el * q 4 el * 2 q 2 el * q 3 el * + 12 q 2 el (2^* - 2 q 4 el (2^* - 2 q 1 el * q 2 el * - 2 q 3 el * q 4 el * + 2 q 1 el * q 3 el * - 2 q 4 el * q 2 el * + 2 q 1 el * q 2 el * 2 q 3 el * q 4 el * + 12 q 2 el (2^* - 2 q 3 el (2^* - 33 mat : 0.734 0.666 - 0.133 0.133 - 0.333 - 0.933 - 0.666 0.667 0.333 - 33 mat

a 6 :

b 3 :

m 20 :

u v Torus a b v cos * + (u cos * a b v cos * + (u sin * b v sin * 31 mat :

TORUS u v Torus 0 0.5 π * 02 π * m m CreateMesh : Slice u v Torus 0.5 π * 1 π * 02 π * m m CreateMesh : 21 line

zoom 0.75 :

Quaternion => α,β

zoom TORUS * quat * zoom Slice * quat * 2 1 sys

http://juliusdavies.ca/andre/permutations.html

a,b,c,d a,b,d,c a,c,b,d a,c,d,b a,d,b,c a,d,c,b b,a,c,d b,a,d,c b,c,a,d b,c,d,a b,d,a,c b,d,c,a c,a,b,d c,a,d,b c,b,a,d c,b,d,a c,d,a,b c,d,b,a d,a,b,c d,a,c,b d,b,a,c d,b,c,a d,c,a,b d,c,b,a

-0.267,-0.535,-0.802,0.267 -0.267,-0.535,0.267,-0.802 -0.267,-0.802,-0.535,0.267 -0.267,-0.802,0.267,-0.535 -0.267,0.267,-0.535,-0.802 -0.267,0.267,-0.802,-0.535 -0.535,-0.267,-0.802,0.267 -0.535,-0.267,0.267,-0.802 -0.535,-0.802,-0.267,0.267 -0.535,-0.802,0.267,-0.267 -0.535,0.267,-0.267,-0.802 -0.535,0.267,-0.802,-0.267 -0.802,-0.267,-0.535,0.267 -0.802,-0.267,0.267,-0.535 -0.802,-0.535,-0.267,0.267 -0.802,-0.535,0.267,-0.267 -0.802,0.267,-0.267,-0.535 -0.802,0.267,-0.535,-0.267 0.267,-0.267,-0.535,-0.802 0.267,-0.267,-0.802,-0.535 0.267,-0.535,-0.267,-0.802 0.267,-0.535,-0.802,-0.267 0.267,-0.802,-0.267,-0.535 0.267,-0.802,-0.535,-0.267