1. Beauty, Form and Function: An Exploration of Symmetry Asset No. 5 Lecture I-4 Point Symmetry PART I Concepts in Symmetry

2. Objectives By the end of this lecture, you will be able to: formally examine reflection and rotation operations in a variety flowers assign the mathematical symbols of 2-fold (diad), 3-fold (triad), 4-fold (tetrad) and 6-fold (hexad) rotation points compose the point symmetry symbols of flowers

3. Rotational Symmetry in Flowers rotation angle = 360 o /2 = 180 o rotation angle = 360 o /4 = 90 o rotation angle = 360 o /3 = 120 o rotation angle = 360 o /6 = 60 o rotation angle = 360 o /5 = 72 o 2 mirror lines (both unique) 3 mirror lines (1 is unique) 4 mirror lines (2 are unique) 6 mirror lines (2 are unique) 5 mirror lines (1 is unique) But.... 5-fold rotation is never used in crystallography. Why is this so? 2mm (both unique) 4mm 3m (not 3mmm) 6mm

4. Summary  Point symmetry involves only reflection and rotation  In assigning point symmetry it is necessary differentiate reflection lines  The point symmetry symbol always has the sequence ‘rotation - mirror type 1 - mirror type 2’ (e.g. 6mm). The symbol is shortened if no rotation is present, or all the mirror lines are identical  The assignment of point symmetry is independent of the object

5. Bibliographies https://encrypted- tbn3.gstatic.com/images?q=tbn:ANd9GcS77WdmjC6W4MB7cOk9 avTNwZcQIzcd9PVOtOh3NhqukVYWJWGp Date retrieved: 9 Jan 2014 http://upload.wikimedia.org/wikipedia/commons/7/7a/Forget-me- not_closeup_2005_01.jpg Date retrieved: 13 Jan 2014 http://upload.wikimedia.org/wikipedia/commons/7/77/Euphorbia _Milii_flowers.jpg

6. Bibliographies https://encrypted- tbn1.gstatic.com/images?q=tbn:ANd9GcQ1e3H4htdWKLvXBYuaq H_CJB-rBDlq8d_CCXRgFlmww4CeqA0M https://encrypted- tbn0.gstatic.com/images?q=tbn:ANd9GcSYf91NGmSsbpz13MFZ cHDaarhamoGHneh1DzhkHpiIgrUVb-sfQQ Date retrieved: 9 Jan 2014