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
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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