Plane Isometries


by MikeDietrich
Tags: isometries, plane
MikeDietrich
MikeDietrich is offline
#1
Dec12-10, 06:41 PM
P: 31
1. The problem statement, all variables and given/known data
Draw two plane figures, each having a 12 element group of symmetries, such that the two groups are NOT isomorphic. Demonstrate that they are not isomorphic.


2. Relevant equations
I know that every finite group of isometries of the plane is isomorphic to either Z_n or to the dihedral group D_n.



3. The attempt at a solution
I drew a regular hexagon (D_6) but now I am stuck as to what to draw for a figure to represent Z_12. Would a 12 bladed windmill (pinwheel) type shape with pronged ends work?
Phys.Org News Partner Science news on Phys.org
Lemurs match scent of a friend to sound of her voice
Repeated self-healing now possible in composite materials
'Heartbleed' fix may slow Web performance
ystael
ystael is offline
#2
Dec12-10, 10:09 PM
P: 352
Yes, this will work, since it is not preserved by a reflection.


Register to reply

Related Discussions
Isometries Proofs Differential Geometry 6
Isometries Calculus & Beyond Homework 0
isometries Calculus & Beyond Homework 6
Decomposing Isometries Linear & Abstract Algebra 2
All isometries of the n-torus Differential Geometry 3