# Difference between revisions of "Talk:Rotational and Reflectional Symmetry in Escher’s Sketches"

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− | + | ==== Solutions ==== | |

− | + | 4. Has reflections. Rotation: 3 fold at point of cap, 3 fold at left sleeve. | |

− | + | 12. This sketch of butterflies is tricky! There are several symmetries that are "almost" there. The reflections do not extend over the entire tessellation, and there is not quite 4-fold symmetry. (The decorations on the wings don't work and there's a problem with how the wings overlap as well) | |

− | + | 13. Has reflections. Rotation: 4 fold where wings meet. 2 fold where heads/tails meet. | |

− | + | ||

− | + | 25. No reflection. 3 fold rotation at right knee, left eye, left back toe. | |

+ | |||

+ | 35. No reflection. 4 fold where heads/tails come together. 2 fold at left elbow. | ||

+ | |||

+ | 45. Has reflection. Rotation 4 fold at wing tips. Order 2 at angel's feet. | ||

+ | |||

+ | 85. Has reflection. Three different centers of order 3 rotation, where heads come together of each colored animal. | ||

+ | |||

+ | 91. Has reflection. No rotation. | ||

+ | |||

+ | Q1. Sketch 44, 57, 99. You've got to ignore the coloring. |

## Latest revision as of 15:31, 22 June 2020

#### Solutions

4. Has reflections. Rotation: 3 fold at point of cap, 3 fold at left sleeve.

12. This sketch of butterflies is tricky! There are several symmetries that are "almost" there. The reflections do not extend over the entire tessellation, and there is not quite 4-fold symmetry. (The decorations on the wings don't work and there's a problem with how the wings overlap as well)

13. Has reflections. Rotation: 4 fold where wings meet. 2 fold where heads/tails meet.

25. No reflection. 3 fold rotation at right knee, left eye, left back toe.

35. No reflection. 4 fold where heads/tails come together. 2 fold at left elbow.

45. Has reflection. Rotation 4 fold at wing tips. Order 2 at angel's feet.

85. Has reflection. Three different centers of order 3 rotation, where heads come together of each colored animal.

91. Has reflection. No rotation.

Q1. Sketch 44, 57, 99. You've got to ignore the coloring.