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2. Rotation formalisms in three dimensions - Wikipedia

   en.wikipedia.org/wiki/Rotation_formalisms_in...

   Rotation formalisms are focused on proper (orientation-preserving) motions of the Euclidean space with one fixed point, that a rotation refers to.Although physical motions with a fixed point are an important case (such as ones described in the center-of-mass frame, or motions of a joint), this approach creates a knowledge about all motions.

3. Solid of revolution - Wikipedia

   en.wikipedia.org/wiki/Solid_of_revolution

   Rotating a curve. The surface formed is a surface of revolution; it encloses a solid of revolution. Solids of revolution (Matemateca Ime-Usp)In geometry, a solid of revolution is a solid figure obtained by rotating a plane figure around some straight line (the axis of revolution), which may not intersect the generatrix (except at its boundary).

4. Surface of revolution - Wikipedia

   en.wikipedia.org/wiki/Surface_of_revolution

   A portion of the curve x = 2 + cos(z) rotated around the z-axis A torus as a square revolved around an axis parallel to one of its diagonals.. A surface of revolution is a surface in Euclidean space created by rotating a curve (the generatrix) one full revolution around an axis of rotation (normally not intersecting the generatrix, except at its endpoints). [1]

5. Toroid - Wikipedia

   en.wikipedia.org/wiki/Toroid

   A toroid using a square. A torus is a type of toroid.. In mathematics, a toroid is a surface of revolution with a hole in the middle. The axis of revolution passes through the hole and so does not intersect the surface. [1]

6. Rotational symmetry - Wikipedia

   en.wikipedia.org/wiki/Rotational_symmetry

   These rotations form the special orthogonal group SO(m), the group of m × m orthogonal matrices with determinant 1. For m = 3 this is the rotation group SO(3) . In another definition of the word, the rotation group of an object is the symmetry group within E + ( n ) , the group of direct isometries ; in other words, the intersection of the ...

7. Torus - Wikipedia

   en.wikipedia.org/wiki/Torus

   Poloidal direction (red arrow) and toroidal direction (blue arrow) A torus of revolution in 3-space can be parametrized as: [2] (,) = (+ ⁡) ⁡ (,) = (+ ⁡) ⁡ (,) = ⁡. using angular coordinates , [,), representing rotation around the tube and rotation around the torus' axis of revolution, respectively, where the major radius is the distance from the center of the tube to the center of ...