Answer to Question #253 in Geometry for Mike




 How many symmetry planes a regular (a) octahedron, (b) dodecahedron, (c) icosahedron has?
(a)The regular octahedron has 3 symmetry planes;  
(b)The regular dodecahedron has 15 symmetry planes;  
(c)The regular icosahedron has 15 symmetry planes;
hi [@banati.bodo](/u/banati.bodo)

the key here is to find which points are on the symmetry plane and keep them there with an onplane goal, then for the points ‘above’ the symmetry plane, use a transform goal to lock them to their mirror image below the symmetry plane.

[symmetry\_planarhex.gh](/uploads/short-url/wlxtpug6o3kghsxsd43l0qwa6jy.gh) (17.3 kb)

[symmetry] answer: 15
solution: there are six straight lines `l\_(1),l\_(2),l\_(3),l\_(4),l\_(5),l\_(6)` in a plane.   
 since no two lines are parallel and no three of which pass through the same point, we have maximum points of intersection.   
 line `l\_(1)` intersect five lines, so there will be five points of intersection.   
 similarly, for each of the lines `l\_(2),l\_(3),l\_(4),l\_(5),l\_(6)`, there will be five points of intersection.   
 but there will be double counting .   
 so, total number of points of intersection is `(5xx6)/(2)=15` Because it is more familiar to you. You have 10 fingers, 10 toes, two eyes, two ears, two arms, two legs, etc. Yes, you have one nose and one mouth but the number two satisfies your natural sense of symmetry more easily. The reason that five is comfortable is because of five fingers and five toes. a - ii, b - iv, c - i, d - iii we know that- - - - - (i)taking 3 as common, we get3; solving only bracket term first,here a = 2a, b = 3b; putting values in eq.i}applying }}ans: - 3}note: must memorize cubes upto 12 a, b and c sin(theta) = d, 
cos(theta) = a, 
tan(theta) = h, 
csc(theta) = f, 
sec(theta) = c, 
cot(theta) = g. answer: k=7 falseno, they are not congruentbecause in kaleidoscope the lenses get biggerso the radii of circle also get biggerhence; they can’t overlap each other chapter 5 key: electron: e                         number: # ­                 valence electron: ve   three­dimensional: 3d molecular: molec               with: w/ chemical: chem                 different: diff positive: pos negative: neg i. bonding theories ­ a. valence shell e pair repulsion (vsepr)  valence shell e pair repulsion: model predicting the arrangements of ve  ­ pairs around a central atom that minimizes their mutual repulsion  electron pair geometry: 3d arrangements of bonding pairs andn lone pairs  of e about a central atom  molecular geometry: 3d arrang