Question

Find something with symmetry (beyond identity) in your apartment/house/living space. Take a picture of it and attach

a) What is the point group?

b) What symmetry elements does it have?

c) Is there function or purpose for the symmetry? If so, how does symmetry affect the function?

Answer 1

Moleculen mmelri Studuve Some chenu hopertes Used wih our to predict vibahonat speca for the danificshon of melewlan shape , ard 8 Caot tine

Aa

o Jio 4G LTE 12:27 PM O 27%) a unf.edu Group Theory: mathematical treatment of symmetry symmetry operation an operation performed on an object which leaves it in a configuration that is indistinguishable from, and superimposable on, the original configuration symmetry elements the points, lines, or planes to which a symmetry operation is carried out Operation Identity Element Identity Symmetry plane Reflection in the plane Inversion center Inversion of a point x,y,z to -x,-y-z Proper axis Rotation by (360/m) Improper axis Symbol 1. Rotation by (360/n) Sn proper axis2 Rfection in plane perpendicular to rotation axis per axes of rotation( Rotation with respect to a line (axis of rotation) Cn is a rotation of (360/n)° C 180 rotation, C-120 rotation, C90° rotation, Cs 72" rotation, C60 rotation. Each rotation brings you to an indistinguishable state from the original However, rotation by 90° about the same axis does not give back the identical molecule Therefore H20 does NOT possess a Ca symmetry axis. XeF, is square planar It has four different C2 axes A C4 axis out of the page is called the principle axis because it has the largestn By convention, the principle axis is in the z-direction 1 of 19 AV point group Done

A
mnety pont noup So0 ejmne axes cut b plane of イnekode Mathematical 130 ups pica dane Symetic elemants Tovp cs →も,on ed-plane c; → E, inversion enten one Lineple) n-foldlaxis one Crnineiple)p )n -told axis one Oh plane one Sn-fold axis which? S Colnadert with Cn osis
eaa
note fnversiem center n C2 axes / one Ơn plane,no planes ove Sn-fold ats Fallows from the Cna.xIS and Plane For n=2/ 41 b) the7eis also notehe S axis E one pauindipal h-fold axis fold ais S so an nven Cant hoctahedra

attet th tunction? -He main ftune of nature, that- astvicts tha penni 3ble dmanie lauws The Cmmapt of balance 1s needed on both feat Rnd a symmetic balance t The la of natore s also loeD on mmatuy bnatiry

to the -Axis s called aun to -the functhiom Since f C-χ)= f(X),this Rnchm -Axis pesbwlan 1ふれ、s expect-to +tting additWe aneas of matumaticl the theo espec