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Cube


Chmutov 01:

$X^4 + $Y^4 + $Z^4 - ($X^2 + $Y^2 + $Z^2 -0.3)
Chmutov 02:

2*($X^2*(3-4*$X^2)^2+$Y^2*(3-4*$Y^2)^2+$Z^2*(3-4*$Z^2)^2) -3
Chmutov 03:

-($X^16 + $Y ^16 + $Z^16 ) +(cosd(2*7*$X) +cosd(7*$Y) +cosd(7*$Z)) +.1
Bretzel Cube:

(($X^4+$Y^4-1)^2+($Z^4-1)^2) * (($Y^4+$Z^4-1)^2+($X^4-1)^2) * (($Z^4+$X^4-1)^2+($Y^4-1)^2) -0.06
C8 Cube:

(8*$X*$X*($X*$X-1) + 1)^2 + (8*$Y*$Y*($Y*$Y-1) + 1)^2 + (8*$Z*$Z*($Z*$Z-1) + 1)^2 - 1
Cage 01:

if( (cos(deg(3*$X))/0.9)^20+(cos(deg(3*$Y))/0.9)^20+(cos(deg(3*$Z))/0.9)^20-1>0,abs(($X^100+$Y^100+$Z^100)^0.01-3.801 )-0.1 , 1)
Cage 02:

( abs(min(min(abs($X),abs($Y)),abs($Z)) - floor(min(min(abs($X),abs($Y)),abs($Z))+0.5) ) * cos(deg($PI/4)) + abs(min(min(max(abs($X),abs($Y)),max(abs($X),abs($Z))),max(abs($Y),abs($Z)) )-floor(min(min(max(abs($X),abs($Y)),max(abs($X),abs($Z))),max(abs($Y),abs($Z)) )+0.5))*sin(deg($PI/4))-sqrt(2)/4 )^2+(max(max(abs($X),abs($Y)),abs($Z))-4.4)^2-0.01
Cage 03:

min( abs( abs( min( min( abs($X), abs($Y)), abs($Z))) -2)* cos( deg($PI/4))+ abs( abs( min( min( max( abs($X), abs($Y)), max( abs($X), abs($Z))), max( abs($Y), abs($Z)) ))-2)*sin(deg($PI/4))-0.4 , min( abs( abs( min( min( abs($X), abs($Y)), abs($Z)))-2), abs( abs( min( min( max( abs($X), abs($Y)), max( abs($X), abs($Z))), max( abs($Y), abs($Z)) ))-2)) )^2+(max(max(abs($X),abs($Y)),abs($Z))-3.4)^2-0.0225
Cage 04:

min(abs(abs(min(min(abs($X),abs($Y)),abs($Z)))-2)*cos(deg($PI/4))+abs(abs(min(min(max(abs($X),abs($Y)),max(abs($X),abs($Z))),max(abs($Y),abs($Z)) ))-2)*sin(deg($PI/4))-0.4,min(abs(abs(min(min(abs($X),abs($Y)),abs($Z)))-2),abs(abs(min(min(max(abs($X),abs($Y)),max(abs($X),abs($Z))),max(abs($Y),abs($Z)) ))-2)))^2+max(max(min( sqrt((max(abs($X),abs($Y))-3)^2+(abs($Z)-3)^2)-1,min(abs($Z)-3,max(abs($X),abs($Y))-3)),abs($Z)-4),max(min( sqrt((abs($X)-3)^2+(abs($Y)-3)^2)-1,min(abs($X)-3,abs($Y)-3) ),max(abs($X),abs($Y))-4 ))^2-0.0225
Cage 05:

(min(abs(abs(min(min(abs($X),abs($Y)),abs($Z)))-2)*cos(deg($PI/4))+abs(abs(min(min(max(abs($X),abs($Y)),max(abs($X),abs($Z))),max(abs($Y),abs($Z)) ))-2)*sin(deg($PI/4))-0.4,min(abs(abs(min(min(abs($X),abs($Y)),abs($Z)))-2),abs(abs(min(min(max(abs($X),abs($Y)),max(abs($X),abs($Z))),max(abs($Y),abs($Z)) ))-2)))-0.3)^2+max(max(min( sqrt((max(abs($X),abs($Y))-3)^2+(abs($Z)-3)^2)-0.7,min(abs($Z)-3,max(abs($X),abs($Y))-3)),abs($Z)-3-0.7 ),max(min( sqrt((abs($X)-3)^2+(abs($Y)-3)^2)-0.7,min(abs($X)-3,abs($Y)-3)),max(abs($X),abs($Y))-3.7))^2-0.0225
Diamond Cage:

 100*($X^22+$Y^22+$Z^22 -($X^22+$Y^22+$Z^22)^2) -31+8*(cos(deg(20*$X)) +cos(deg(20*$Y)) +cos(deg(20*$Z)))
Fresnel Sphere 01:

cosd(abs($X^2+$Y^2+$Z^2))


Fresnel Sphere 02:

sind(4*$PI*( sqrt((cosd($X) + cosd($Y) )^2+$Z^2) -0.3 ))
Fresnel Sphere 03:

sind( 2*$PI*( cosd($X)+cosd($Y)+cosd($Z) ))
Sphere Minus Cube:

($X^2 + $Y^2 + $Z^2 - 1) * max( max( $Y^2-1, $X^2-1 ), $Z^2-1 )
Sphere Minus Cube Soft:

 ((1/2.3)^2 *($X^2 + $Y^2 + $Z^2))^-6 + ( (1/2)^8 * ($X^8 + $Y^8 + $Z^8) )^6 -1
Styled Cubus:

-2/125 +$X^16 +$Y^16 +$Z^16 -2*$X^12 -2*$Y^12 -2*$Z^12 +1.25*$X^4 +1.25*$Y^4 +1.25*$Z^4-0.25*$X^2 -0.25*$Y^2 -0.25*$Z^2+0.03125
Tangle:

$X^4 - ch("a") *$X^2 + $Y^4 - 5*$Y^2 + $Z^4 - ch("a") *$Z^2 + ch("b")

Where a and b values are parameters.
Tooth:

$X^ch("a") +$Y^ch("a") +$Z^ch("a") -($X^ch("b")+$Y^ch("b")+$Z^ch("b"))

Where a and b values are parameters.

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