91 



A cylindrical flask filled with a hypothetical, homogeneous, and 

 weightless liquid, may be mentioned as an instance of a system 

 having the symmetry D . 



The group Cg possesses: a homopolar axis of isotropy A^, 

 a plane of symmetry perpendicular to it, and a symmetry-centre, but 

 no planes of symmetry passing through A^. 



If a cylinder with circular base be rotated round its axis in a 



2. 



Group 



vsfcL I -jJ 

 Group CH. 



3. & 



Group 



(Holohedrism). (Pyramidal Hemihedrism). (Trapezohedral Hemihedrism). 



' A ,. 



5. 



Group C. Group C M . 



(Hemimorphic Hemihedrism.) (Hernimorphic Tetartohedrism) . 



Fig. 94. 



Symmetry-Groups with a single Axis of Isotropy. 



definite direction with a constant angular velocity, the body as a 

 whole may be said to have the symmetry of the group Cg . Indeed, 

 if the rotating cylinder be reflected in a plane perpendicular to its 

 axis of revolution, the mirror-image is congruent with the cylinder 

 itself, while the image changes in no way by a rotation through an 

 angle of 180 round an axis perpendicular to the reflecting plane. 



