Wallpaper Symmetries CS 39 Carlo H. Séquin

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Presentation transcript:

Wallpaper Symmetries CS 39 Carlo H. Séquin Florida 1999 CS 39 Wallpaper Symmetries Carlo H. Séquin EECS Computer Science Division University of California, Berkeley A chose a very mathematical title …

Wallpaper Symmetries Worksheet

Take One Pattern at a Time . . . Find rotation centers, mirror lines, glide axes

Take One Pattern at a Time . . . Pure Rotation: 3 Mirror Line Kaleidoscope Point: 3 >> Symm.: 3*3 Find all unique rotation centers, mirror lines, glide axes

Different Kaleidoscope Points Count different ones individually!

3 Different Kaleidoscope Points Symmetry: *442

Take One Pattern at a Time . . . Find rotation centers, mirror lines, glide axes

Take One Pattern at a Time . . . Pure Rotation: 2 Pure Rotation: 2 Glide Axis >> Symm.: 22X Find all unique rotation centers, mirror lines, glide axes

Take One Pattern at a Time . . . Find rotation centers, mirror lines, glide axes

Take One Pattern at a Time . . . Mirror Line Glide Axis >> Symm.: *X Find all unique rotation centers, mirror lines, glide axes

Different Glide Axes ? Find rotation centers, mirror lines, glide axes

Two Different Glide Axes Glide Axis Glide Axis >> Symm.: XX Find all unique rotation centers, mirror lines, glide axes