During computer analysis of the stereoradiographs, the position of the object with respect to its reference landmarks is described as translations along, and rotations about, all three orthogonal axes in the Cartesian coordinate system.
In the commercial versions of the puzzle, an internal system of pivots allows any layer of nine cubelets to be rotated with respect to the rest, so that successive rotations about the three axes cause the cubelet faces to become scrambled.
Rotations about carbon-carbon bonds interconvert two equally energetic chair forms.
As complexity increases, isomerism induced by rotations about bonds becomes a bigger factor.
That is to say, rotations about this axis by 72° leave the appearance of the grain unchanged.
Once each supercontinent is assembled, it undergoes back-and-forth rotations about a stable axis on the Equator, Mr. Mitchell said.
This distortion involves no more than rotations about carbon-carbon bonds, just as occurs in ethane or any other acyclic alkane.
For example, in Euclidean three-dimensional space, rotations leave unaltered the distances between points; the set of all rotations about a fixed point turns out to form a Lie group, and it is one of the Lie groups in the classification.
Rotations about single points and lines are possible.
Most of these misorientations occurred by rotations about the transverse direction ∥〈1 1 0〉 axis with significant further rotations about 〈1 1 2〉 poles.
The model involves internal backbone rotations about axes between C-alpha atoms.
