EMS162_2010_InfiniteSymmetryElements

EMS162_2010_InfiniteSymmetryElements - Mirror plane ⊥ to...

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1 1/14/2010 EMS 162 - Winter 2010 14 Yayoi Takamura Glide Planes • a-glide plane: mirror plane perpendicular to b - axis or c - axis + translation along a -axis by ½ a Translation vector, a Shift = ½ Mirror b -axis Mirror c -axis (x,y,z) (x + ½,-y,z) (x,y,z) (x + ½,y,-z) 1/14/2010 EMS 162 - Winter 2010 15 Yayoi Takamura Glide Planes • n-glide plane: mirror plane perpendicular to a -, b - or c - axis + translation along diagonal by ½ d d=a+b, d=a-b, d=a+b+c, etc… e.g.: mirror plane c- axis + translate ½ ( a+b ) (x,y,z) (x + ½, y + ½, -z)
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2 1/14/2010 EMS 162 - Winter 2010 16 Yayoi Takamura n -Glide Planes Translation vector, b Shift = ½ ( b+c ) (x,y,z) (-x,y + ½,z + ½)
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Unformatted text preview: Mirror plane ⊥ to a-axis Mirror plane ⊥ to b-axis Translation vector, a Shift = ½ ( a+c ) (x,y,z) (x + ½, -y, z + ½) 1/14/2010 EMS 162 - Winter 2010 17 Yayoi Takamura Screw Axis • Combination of rotation + translation parallel to the rotation axis – Rotation, ϕ =360°/ N where N =1, 2, 3, 4, 6 – Translation, t = k / N where 1 < k < N-1 Side view Top view 2 1 screw axis 3 1/14/2010 EMS 162 - Winter 2010 18 Yayoi Takamura 3-Fold Screw Axis clockwise counter clockwise Translation vector, c Shift = 1/3 Shift = 2/3...
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EMS162_2010_InfiniteSymmetryElements - Mirror plane ⊥ to...

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