Difference between revisions of "Escher's Wallpaper Groups Exploration"
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{{objective|Learn to recognize the lattice in a wallpaper pattern. Learn to use the flow chart to identify wallpaper symmetry groups.}} | {{objective|Learn to recognize the lattice in a wallpaper pattern. Learn to use the flow chart to identify wallpaper symmetry groups.}} | ||
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| + | ==Materials== | ||
| + | {{printable|Printed version of the Escher's Wallpaper Groups Exploration, dimmed: [[Image:Eschertessellations.pdf]]}} | ||
| + | * Printed copy of the Escher's Wallpaper Groups Exploration. | ||
| + | {{clear}} | ||
| + | |||
| + | ==Exploration== | ||
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In this exploration we will look at the wallpaper patterns in {{VOS}} and use the flowchart to determine their wallpaper group. | In this exploration we will look at the wallpaper patterns in {{VOS}} and use the flowchart to determine their wallpaper group. | ||
Revision as of 14:42, 14 September 2008
Objective: Learn to recognize the lattice in a wallpaper pattern. Learn to use the flow chart to identify wallpaper symmetry groups.
Materials
- Printed copy of the Escher's Wallpaper Groups Exploration.
Exploration
In this exploration we will look at the wallpaper patterns in Visions of Symmetry and use the flowchart to determine their wallpaper group. First we will identify the largest order rotation for the tessellation, and check if there are reflections and glide-reflections. This is the data we need to use the flowchart.
Several examples from Visions of Symmetry:
- Drawing #1: The largest order rotation is 2. There are no reflections or glide-reflections. Following the flow chart we end up at p2.
- Drawing #2: The largest order rotation is 2. There are no reflections, but there are glide-reflections. Following the flow chart we end up at pgg.
- Drawing #3: The largest order rotation is 4. There are reflections, and there are glide-reflections. Following the flow chart we end up at p4g. (The mirror lines meet at 90 degree angles, not at 45 degree angles.)
- Drawing #4: The largest order rotation is 3. There are reflections, but there are no glide-reflections. Following the flow chart we end up at p31m. (The centers of rotation at the hands do NOT lie on the mirror lines.)
| Escher Drawing | Rotation | Reflection | Glide-Reflection | Symmetry group |
|---|---|---|---|---|
| Visions of Symmetry #1, pg 116 | 2-fold | No | No | p2 |
| Visions of Symmetry #2, pg 116 | 2-fold | No | Yes | ppg |
| Visions of Symmetry #3, pg 117 | 4-fold | Yes | Yes | p4g |
| Visions of Symmetry #4, pg 118 | 3-fold | Yes | No | p31m |
| Visions of Symmetry #6, pg 120 | ||||
| Visions of Symmetry #9, pg 123 | ||||
| Visions of Symmetry #13, pg 126 | ||||
| Visions of Symmetry #16, pg 128 | ||||
| Visions of Symmetry #20, pg 131 | ||||
| Visions of Symmetry #28, pg 137 | ||||
| Visions of Symmetry #37, pg 145 | ||||
| Visions of Symmetry #42, pg 148 | ||||
| Visions of Symmetry #43, pg 149 | ||||
| Visions of Symmetry #44, pg 151 | ||||
| Visions of Symmetry #45, pg 150 | ||||
| Visions of Symmetry #70, pg 142 | ||||
| Visions of Symmetry #81, pg 181 | ||||
| Visions of Symmetry #91, pg 190 |
Handin: A sheet with answers to all questions.
Escher's Wallpaper Groups Solutions (Instructors only)
