Surfaces of higher order

An algebraic surface of higher order n in real 3-dimensional space is the set of zeros of a polynomial in 3 variables of degree n>3. The surfaces 123-125 are Kummer surfaces named after the Berlin mathematician (1810-1893). They are of order 4 and have 16 not necessarily real double points. The surfaces 126-131 are made by Kummer. The cyclides (models 153-162) are algebraic surfaces of order 4. They are also of interest in differential geometry.

Img(78) CylindroidImg(79) Cylindroid combined with a right-angled paraboloid
Img(87) Developable surface of higher orderImg(88) Developable surface of higher order
Img(89) Developable surface of higher orderImg(90) Developable surface of higher order
Img(91) Developable surface of higher orderImg(92) Developable surface of higher order
Img(93) Developable surface of higher orderImg(94) Developable surface of higher order
Img(122) Cylindroid made of carton discsImg(123) Kummer surface with 8 real double points
Img(124) Kummer surface with 16 double pointsImg(125) Kummer areas with 8 respectively 16 respectively 4 real intersections
Img(126) Surface of 4. order with 4 planes touching along circlesImg(127) Areas of 4. order with 4 circles touching along the plane
Img(128) Surface of 4. order with 4 planes touching along ciclesImg(129) Surface of 4. order with 4 planes touching along cicles
Img(130) Surface of 4. order with 4 planes touching along ciclesImg(131) Surface of 4. order with 4 planes touching along cicles
Img(132) Surface of 4. order with a double lineImg(133) Surface of 4. order with double lines
Img(134) Surface of 8. orderImg(151) Chord central point area of a space curve of 4. order.
Img(152) Surface of 12. orderImg(153) Ring cyclide of Dupin
Img(154) Cyclide of Dupin Img(155) Cyclide of Dupin
Img(156) Horn cyclide of DupinImg(157) Spindel cyclide of Dupin
Img(158) Parabolic horn cyclide of DupinImg(159) Cyclide of Dupin
Img(160) Cyclide with two conjugated imaginary double pointsImg(161) Cyclide with two conjugated imaginary double points and a real double point
Img(162) Cyclide with a uniplanar double pointImg(302) Surface of 5. order with many symmetry attributes
Img(371) Spherical torus of circular brass wires