Mathematical Crystallography And the Theory of Groups of Movements
Mathematical Crystallography And the Theory of Groups of Movements
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181 to 188).
The [le arrangement of the axes of IT is that of Fig. 91 ; and since the opexutions of U and F brinff this system of axes into self-comcidence, the axes of U and F must be parallel to the diagonals of the rhombus of that figure.
In the group whose subgroups are C^^ C^\ C^ the axes of W are au screw-axes, and therefore no two rotation-axes of U and F can meet. Since, however, a rotation about one of ihe rotation-axes of U, followed by a rotation about any one of the rotation-axes of... F, is equivalent to a screw aboi^ a line meeting both axes, therefore the screw-axes of W cut * Exoept in the ease of Fig. 128, when the sides of the pandlelepiped *" i^-» *Tf> in« ORTHOEHOMBIC GROUPS 191 rotation-axes of TI and F. These considerations show that the arrangement of axes must be that of Fig: 121.
Q«. Subgroups C^\G^,C^.
If however the axes of W are rotation-axes, the rotation- axes of U and V must intersect, and axes of W must pass through their points of intersection; this leads at once to Fig.
What to read after Mathematical Crystallography And the Theory of Groups of Movements?
You can find similar books in the "Read Also" column, or choose other free books by Hilton, Harold, B.1876- to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
181 to 188).
The [le arrangement of the axes of IT is that of Fig. 91 ; and since the opexutions of U and F brinff this system of axes into self-comcidence, the axes of U and F must be parallel to the diagonals of the rhombus of that figure.
In the group whose subgroups are C^^ C^\ C^ the axes of W are au screw-axes, and therefore no two rotation-axes of U and F can meet. Since, however, a rotation about one of ihe rotation-axes of U, followed by a rotation about any one of the rotation-axes of... F, is equivalent to a screw aboi^ a line meeting both axes, therefore the screw-axes of W cut * Exoept in the ease of Fig. 128, when the sides of the pandlelepiped *" i^-» *Tf> in« ORTHOEHOMBIC GROUPS 191 rotation-axes of TI and F. These considerations show that the arrangement of axes must be that of Fig: 121.
Q«. Subgroups C^\G^,C^.
If however the axes of W are rotation-axes, the rotation- axes of U and V must intersect, and axes of W must pass through their points of intersection; this leads at once to Fig.
What to read after Mathematical Crystallography And the Theory of Groups of Movements?
You can find similar books in the "Read Also" column, or choose other free books by Hilton, Harold, B.1876- to read onlineMoreLess
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