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Answers. Some answers to some exercises. Answers to exercise 2. The sum of the angels of a triangle equals 180 o. The sum of the angels of a quadrilateral equals 360 o Why ? n = 4 and (4 – 2) x 180 o = 360 o. Answers to exercise 2. n = 15 and (15 – 2) x 180 o = 2340 o.

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  1. Answers Someanswers to someexercises

  2. Answers to exercise 2 • The sum of the angels of a triangleequals 180o • The sum of the angels of a quadrilateralequals 360o • Why? n = 4 and (4 – 2) x 180o = 360o

  3. Answers to exercise 2 n = 15 and (15 – 2) x 180o = 2340o • The sum of the angels of a pentagonequals 520o • Why? n = 5 and (5 – 2) x 180o = 520o

  4. Answer to exercise 3:is it possible to make a monohedral tiling with every triangle ? • yes

  5. Answer to exercise 3:is it possible to make a monohedral tiling with every quadrilateral ? • yes

  6. Answer to exercise 3:is it possible to make a monohedral tiling with every quadrilateral ? tessellation with arbitrary quadrilateral

  7. Answer to exercise 5

  8. Answer to exercise 5

  9. Answerexercise 6two of manypossibilities

  10. Answerexercise 6two of manypossibilities

  11. Answersexercise 7 Reflections(ignoring the short diagonallinesbetween the ovals), norotations rotations over 90oand180o, noreflections

  12. Answers exercise 7 reflections rotations over 60o, 120o and180o

  13. Answerexercise 8 • The onlysymmetry of the parallelogram is rotation over 180o. • No reflectionsymmetries

  14. Answerexercise 8 • A rectangle is a special kind of parallelogramsoit has rotational symmetrie over 180o. • Moreover is has two mirror axesperpendicular to the edges

  15. Answerexercise 8 • A rhombus is a special kind of parallelogramsoit has rotational symmetrie over 180o. • Moreover is has two mirror axesthrough the vertices

  16. Answerexercise 8 • A square is a special kind of parallelogramsoit has rotational symmetrie over 180o. • A square is a special kind of rectangle, so is has two mirror axesperpendicular to the edges. • A square is a special kind of rhombus, so is has two mirror axesthrough the vertices. • Moreoverit has rotational symmetrie over 90o

  17. Answerexercise 8 • The hexagon has rotationalsymmetry over 60o. • And several mirror axes

  18. Answerexercise 10 what does the lattice look like? what is the shape of the fundamental domain what symmetries come with a square? Reflection and rotation over 90o.

  19. Answerexercise 10 can the fundamental domain be constructed out of one smaller figure, a primitive cell? what symmetry operations are necessary to cover the fundamental domain with this primitive cell without gaps or overlaps? a reflection over the hypotenuse fourrotations over 90o.

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