Consider the labelled pentagon
For each of the following permutations, determine if the permutation is a symmetry of the pentagon in flatland, sphereland (3 dimenions), or if the transformation is never a symmetry.
Where is the permutation \begin{pmatrix} 1&2&3&4&5\\1&2&3&4&5\end{pmatrix} a symmetry of the above figure, if at all?
I do not know yet
Flatland
Sphereland, but not Flatland
This permutation is not a symmetry
Where is the permutation \begin{pmatrix} 1&2&3&4&5\\2&3&4&5&1\end{pmatrix} a symmetry of the above figure, if at all?
I do not know yet
Flatland
Sphereland, but not Flatland
This permutation is not a symmetry
Where is the permutation \begin{pmatrix} 1&2&3&4&5\\2&1&5&4&3\end{pmatrix} a symmetry of the above figure, if at all?
I do not know yet
Flatland
Sphereland, but not Flatland
This permutation is not a symmetry
Where is the permutation \begin{pmatrix} 1&2&3&4&5\\3&2&4&1&5\end{pmatrix} a symmetry of the above figure, if at all?
I do not know yet
Flatland
Sphereland, but not Flatland
This permutation is not a symmetry
Where is the permutation \begin{pmatrix} 1&2&3&4&5\\4&5&1&2&3\end{pmatrix} a symmetry of the above figure, if at all?
I do not know yet
Flatland
Sphereland, but not Flatland
This permutation is not a symmetry
Where is the permutation \begin{pmatrix} 1&2&3&4&5\\5&4&3&2&1\end{pmatrix} a symmetry of the above figure, if at all?
I do not know yet
Flatland
Sphereland, but not Flatland
This permutation is not a symmetry
Where is the permutation \begin{pmatrix} 1&2&3&4&5\\5&4&1&3&2\end{pmatrix} a symmetry of the above figure, if at all?
I do not know yet
Flatland
Sphereland, but not Flatland
This permutation is not a symmetry
Find the permutation representing the transformation
from
to
Find the permutation representing the transformation
from
to
Find the permutation representing the transformation
from
to
Is the following statement true, false, or neither?
and are the same pentagon in sphereland
Is the following statement true, false, or neither?
and are the same pentagon in sphereland
Is the following statement true, false, or neither?
and are the same pentagon in sphereland
Is the following statement true, false, or neither?
and are the same pentagon in sphereland
Is the following statement true, false, or neither?
and are the same pentagon in sphereland
Is the following statement true, false, or neither?
and are the same pentagon in sphereland
In the 1993 video game, "Myst", one of the
puzzles involved setting the lock combination below to 313.


However, it's impossible. Show that given a combination $(x,y,z)$, $[x + z  y]_3$ does not change
no matter what button is pushed. Use this to show that the 27 combinations can
be partitioned into 3 equivalence classes of 9 combinations each, and that the initial combination $(1,1,1)$
is not in the same equivalence class as the solution combination $(3,1,3)$.
Can you turn the combination lock below to combination 1211?



Explain.