February 8



Review from last class:
FAPP video on Tilings of the plane.

Symmetry Ideas



Before: A                              After : A  or    B  or     C

Suppose I know where A goes:

What about B?  If A -> A     Before: B   After: B   or C

                          If  A ->B        Before:B     After: A or C

                          If  A ->C       Before: B       After A or B

A goes to
Then B goes to
And C must go to
A
B
C

C
B
B
A
C

C
A
C
A
B

B
A


By an analysis of a "tree" we count there are exactly and only 6 possibilities for where the vertices can be transformed.
         


V*R     =   R2 ?
*
Id
R120
R240
V
G=R1
H=R2
Id
I





R120

R240

R1


R240

I

R2


V

R2
R1
I

R120
G=R1




I

H=R2





I
Do Activity. This shows that R240*V = R1