Simetri ikosahedral
Struktur grup > Isomorfisme I dengan A5

| Matriks rotasi | Permutasi 5 pada 1 2 3 4 5 | Permutasi 12 pada 1 2 3 4 5 6 7 8 9 10 11 12 |
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|  M_{1}={\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}} |  P_{1} = () |  Q_{1} = () |
|  M_{2}={\begin{bmatrix}-{\frac {1}{2}}&{\frac {1}{2\phi }}&{\frac {\phi }{2}}\\-{\frac {1}{2\phi }}&{\frac {\phi }{2}}&-{\frac {1}{2}}\\-{\frac {\phi }{2}}&-{\frac {1}{2}}&-{\frac {1}{2\phi }}\end{bmatrix}} |  P_{2} = (3 4 5) |  Q_{2} = (1 11 8)(2 9 6)(3 5 12)(4 7 10) |
|  M_{3}={\begin{bmatrix}-{\frac {1}{2}}&-{\frac {1}{2\phi }}&-{\frac {\phi }{2}}\\{\frac {1}{2\phi }}&{\frac {\phi }{2}}&-{\frac {1}{2}}\\{\frac {\phi }{2}}&-{\frac {1}{2}}&-{\frac {1}{2\phi }}\end{bmatrix}} |  P_{3} = (3 5 4) |  Q_{3} = (1 8 11)(2 6 9)(3 12 5)(4 10 7) |
|  M_{4}={\begin{bmatrix}-{\frac {1}{2}}&{\frac {1}{2\phi }}&-{\frac {\phi }{2}}\\{\frac {1}{2\phi }}&-{\frac {\phi }{2}}&-{\frac {1}{2}}\\-{\frac {\phi }{2}}&-{\frac {1}{2}}&{\frac {1}{2\phi }}\end{bmatrix}} |  P_{4} = (2 3)(4 5) |  Q_{4} = (1 12)(2 8)(3 6)(4 9)(5 10)(7 11) |
|  M_{5}={\begin{bmatrix}{\frac {\phi }{2}}&{\frac {1}{2}}&{\frac {1}{2\phi }}\\{\frac {1}{2}}&-{\frac {1}{2\phi }}&-{\frac {\phi }{2}}\\-{\frac {1}{2\phi }}&{\frac {\phi }{2}}&-{\frac {1}{2}}\end{bmatrix}} |  P_{5} = (2 3 4) |  Q_{5} = (1 2 3)(4 5 6)(7 9 8)(10 11 12) |
|  M_{6}={\begin{bmatrix}-{\frac {1}{2\phi }}&-{\frac {\phi }{2}}&{\frac {1}{2}}\\{\frac {\phi }{2}}&-{\frac {1}{2}}&-{\frac {1}{2\phi }}\\{\frac {1}{2}}&{\frac {1}{2\phi }}&{\frac {\phi }{2}}\end{bmatrix}} |  P_{6} = (2 3 5) |  Q_{6} = (1 7 5)(2 4 11)(3 10 9)(6 8 12) |
|  M_{7}={\begin{bmatrix}{\frac {\phi }{2}}&{\frac {1}{2}}&-{\frac {1}{2\phi }}\\{\frac {1}{2}}&-{\frac {1}{2\phi }}&{\frac {\phi }{2}}\\{\frac {1}{2\phi }}&-{\frac {\phi }{2}}&-{\frac {1}{2}}\end{bmatrix}} |  P_{7} = (2 4 3) |  Q_{7} = (1 3 2)(4 6 5)(7 8 9)(10 12 11) |
|  M_{8}={\begin{bmatrix}0&-1&0\\0&0&1\\-1&0&0\end{bmatrix}} |  P_{8} = (2 4 5) |  Q_{8} = (1 10 6)(2 7 12)(3 4 8)(5 11 9) |
|  M_{9}={\begin{bmatrix}-{\frac {\phi }{2}}&{\frac {1}{2}}&{\frac {1}{2\phi }}\\{\frac {1}{2}}&{\frac {1}{2\phi }}&{\frac {\phi }{2}}\\{\frac {1}{2\phi }}&{\frac {\phi }{2}}&-{\frac {1}{2}}\end{bmatrix}} |  P_{9} = (2 4)(3 5) |  Q_{9} = (1 9)(2 5)(3 11)(4 12)(6 7)(8 10) |
|  M_{10}={\begin{bmatrix}-{\frac {1}{2\phi }}&{\frac {\phi }{2}}&{\frac {1}{2}}\\-{\frac {\phi }{2}}&-{\frac {1}{2}}&{\frac {1}{2\phi }}\\{\frac {1}{2}}&-{\frac {1}{2\phi }}&{\frac {\phi }{2}}\end{bmatrix}} |  P_{10} = (2 5 3) |  Q_{10} = (1 5 7)(2 11 4)(3 9 10)(6 12 8) |
|  M_{11}={\begin{bmatrix}0&0&-1\\-1&0&0\\0&1&0\end{bmatrix}} |  P_{11} = (2 5 4) |  Q_{11} = (1 6 10)(2 12 7)(3 8 4)(5 9 11) |
|  M_{12}={\begin{bmatrix}{\frac {1}{2\phi }}&-{\frac {\phi }{2}}&{\frac {1}{2}}\\-{\frac {\phi }{2}}&-{\frac {1}{2}}&-{\frac {1}{2\phi }}\\{\frac {1}{2}}&-{\frac {1}{2\phi }}&-{\frac {\phi }{2}}\end{bmatrix}} |  P_{12} = (2 5)(3 4) |  Q_{12} = (1 4)(2 10)(3 7)(5 8)(6 11)(9 12) |
|  M_{13}={\begin{bmatrix}1&0&0\\0&-1&0\\0&0&-1\end{bmatrix}} |  P_{13} = (1 2)(4 5) |  Q_{13} = (1 3)(2 4)(5 8)(6 7)(9 10)(11 12) |
|  M_{14}={\begin{bmatrix}-{\frac {1}{2}}&{\frac {1}{2\phi }}&{\frac {\phi }{2}}\\{\frac {1}{2\phi }}&-{\frac {\phi }{2}}&{\frac {1}{2}}\\{\frac {\phi }{2}}&{\frac {1}{2}}&{\frac {1}{2\phi }}\end{bmatrix}} |  P_{14} = (1 2)(3 4) |  Q_{14} = (1 5)(2 7)(3 11)(4 9)(6 10)(8 12) |
|  M_{15}={\begin{bmatrix}-{\frac {1}{2}}&-{\frac {1}{2\phi }}&-{\frac {\phi }{2}}\\-{\frac {1}{2\phi }}&-{\frac {\phi }{2}}&{\frac {1}{2}}\\-{\frac {\phi }{2}}&{\frac {1}{2}}&{\frac {1}{2\phi }}\end{bmatrix}} |  P_{15} = (1 2)(3 5) |  Q_{15} = (1 12)(2 10)(3 8)(4 6)(5 11)(7 9) |
|  M_{16}={\begin{bmatrix}-{\frac {1}{2}}&-{\frac {1}{2\phi }}&{\frac {\phi }{2}}\\{\frac {1}{2\phi }}&{\frac {\phi }{2}}&{\frac {1}{2}}\\-{\frac {\phi }{2}}&{\frac {1}{2}}&-{\frac {1}{2\phi }}\end{bmatrix}} |  P_{16} = (1 2 3) |  Q_{16} = (1 11 6)(2 5 9)(3 7 12)(4 10 8) |
|  M_{17}={\begin{bmatrix}-{\frac {1}{2\phi }}&{\frac {\phi }{2}}&-{\frac {1}{2}}\\{\frac {\phi }{2}}&{\frac {1}{2}}&{\frac {1}{2\phi }}\\{\frac {1}{2}}&-{\frac {1}{2\phi }}&-{\frac {\phi }{2}}\end{bmatrix}} |  P_{17} = (1 2 3 4 5) |  Q_{17} = (1 6 5 3 9)(4 12 7 8 11) |
|  M_{18}={\begin{bmatrix}{\frac {\phi }{2}}&-{\frac {1}{2}}&-{\frac {1}{2\phi }}\\{\frac {1}{2}}&{\frac {1}{2\phi }}&{\frac {\phi }{2}}\\-{\frac {1}{2\phi }}&-{\frac {\phi }{2}}&{\frac {1}{2}}\end{bmatrix}} |  P_{18} = (1 2 3 5 4) |  Q_{18} = (1 4 8 6 2)(5 7 10 12 9) |
|  M_{19}={\begin{bmatrix}-{\frac {1}{2\phi }}&-{\frac {\phi }{2}}&-{\frac {1}{2}}\\-{\frac {\phi }{2}}&{\frac {1}{2}}&-{\frac {1}{2\phi }}\\{\frac {1}{2}}&{\frac {1}{2\phi }}&-{\frac {\phi }{2}}\end{bmatrix}} |  P_{19} = (1 2 4 5 3) |  Q_{19} = (1 8 7 3 10)(2 12 5 6 11) |
|  M_{20}={\begin{bmatrix}0&0&1\\-1&0&0\\0&-1&0\end{bmatrix}} |  P_{20} = (1 2 4) |  Q_{20} = (1 7 4)(2 11 8)(3 5 10)(6 9 12) |
|  M_{21}={\begin{bmatrix}{\frac {1}{2\phi }}&{\frac {\phi }{2}}&-{\frac {1}{2}}\\-{\frac {\phi }{2}}&{\frac {1}{2}}&{\frac {1}{2\phi }}\\{\frac {1}{2}}&{\frac {1}{2\phi }}&{\frac {\phi }{2}}\end{bmatrix}} |  P_{21} = (1 2 4 3 5) |  Q_{21} = (1 2 9 11 7)(3 6 12 10 4) |
|  M_{22}={\begin{bmatrix}{\frac {\phi }{2}}&-{\frac {1}{2}}&{\frac {1}{2\phi }}\\{\frac {1}{2}}&{\frac {1}{2\phi }}&-{\frac {\phi }{2}}\\{\frac {1}{2\phi }}&{\frac {\phi }{2}}&{\frac {1}{2}}\end{bmatrix}} |  P_{22} = (1 2 5 4 3) |  Q_{22} = (2 3 4 7 5)(6 8 10 11 9) |
|  M_{23}={\begin{bmatrix}0&1&0\\0&0&-1\\-1&0&0\end{bmatrix}} |  P_{23} = (1 2 5) |  Q_{23} = (1 9 8)(2 6 3)(4 5 12)(7 11 10) |
|  M_{24}={\begin{bmatrix}-{\frac {\phi }{2}}&-{\frac {1}{2}}&-{\frac {1}{2\phi }}\\{\frac {1}{2}}&-{\frac {1}{2\phi }}&-{\frac {\phi }{2}}\\{\frac {1}{2\phi }}&-{\frac {\phi }{2}}&{\frac {1}{2}}\end{bmatrix}} |  P_{24} = (1 2 5 3 4) |  Q_{24} = (1 10 5 4 11)(2 8 9 3 12) |
|  M_{25}={\begin{bmatrix}-{\frac {1}{2}}&{\frac {1}{2\phi }}&-{\frac {\phi }{2}}\\-{\frac {1}{2\phi }}&{\frac {\phi }{2}}&{\frac {1}{2}}\\{\frac {\phi }{2}}&{\frac {1}{2}}&-{\frac {1}{2\phi }}\end{bmatrix}} |  P_{25} = (1 3 2) |  Q_{25} = (1 6 11)(2 9 5)(3 12 7)(4 8 10) |
|  M_{26}={\begin{bmatrix}{\frac {\phi }{2}}&{\frac {1}{2}}&{\frac {1}{2\phi }}\\-{\frac {1}{2}}&{\frac {1}{2\phi }}&{\frac {\phi }{2}}\\{\frac {1}{2\phi }}&-{\frac {\phi }{2}}&{\frac {1}{2}}\end{bmatrix}} |  P_{26} = (1 3 4 5 2) |  Q_{26} = (2 5 7 4 3)(6 9 11 10 8) |
|  M_{27}={\begin{bmatrix}-{\frac {1}{2\phi }}&-{\frac {\phi }{2}}&{\frac {1}{2}}\\-{\frac {\phi }{2}}&{\frac {1}{2}}&{\frac {1}{2\phi }}\\-{\frac {1}{2}}&-{\frac {1}{2\phi }}&-{\frac {\phi }{2}}\end{bmatrix}} |  P_{27} = (1 3 5 4 2) |  Q_{27} = (1 10 3 7 8)(2 11 6 5 12) |
|  M_{28}={\begin{bmatrix}-{\frac {1}{2}}&-{\frac {1}{2\phi }}&{\frac {\phi }{2}}\\-{\frac {1}{2\phi }}&-{\frac {\phi }{2}}&-{\frac {1}{2}}\\{\frac {\phi }{2}}&-{\frac {1}{2}}&{\frac {1}{2\phi }}\end{bmatrix}} |  P_{28} = (1 3)(4 5) |  Q_{28} = (1 7)(2 10)(3 11)(4 5)(6 12)(8 9) |
|  M_{29}={\begin{bmatrix}-{\frac {1}{2\phi }}&{\frac {\phi }{2}}&-{\frac {1}{2}}\\-{\frac {\phi }{2}}&-{\frac {1}{2}}&-{\frac {1}{2\phi }}\\-{\frac {1}{2}}&{\frac {1}{2\phi }}&{\frac {\phi }{2}}\end{bmatrix}} |  P_{29} = (1 3 4) |  Q_{29} = (1 9 10)(2 12 4)(3 6 8)(5 11 7) |
|  M_{30}={\begin{bmatrix}{\frac {\phi }{2}}&-{\frac {1}{2}}&-{\frac {1}{2\phi }}\\-{\frac {1}{2}}&-{\frac {1}{2\phi }}&-{\frac {\phi }{2}}\\{\frac {1}{2\phi }}&{\frac {\phi }{2}}&-{\frac {1}{2}}\end{bmatrix}} |  P_{30} = (1 3 5) |  Q_{30} = (1 3 4)(2 8 7)(5 6 10)(9 12 11) |
|  M_{31}={\begin{bmatrix}-{\frac {\phi }{2}}&{\frac {1}{2}}&-{\frac {1}{2\phi }}\\{\frac {1}{2}}&{\frac {1}{2\phi }}&-{\frac {\phi }{2}}\\-{\frac {1}{2\phi }}&-{\frac {\phi }{2}}&-{\frac {1}{2}}\end{bmatrix}} |  P_{31} = (1 3)(2 4) |  Q_{31} = (1 12)(2 6)(3 9)(4 11)(5 8)(7 10) |
|  M_{32}={\begin{bmatrix}{\frac {1}{2\phi }}&-{\frac {\phi }{2}}&-{\frac {1}{2}}\\{\frac {\phi }{2}}&{\frac {1}{2}}&-{\frac {1}{2\phi }}\\{\frac {1}{2}}&-{\frac {1}{2\phi }}&{\frac {\phi }{2}}\end{bmatrix}} |  P_{32} = (1 3 2 4 5) |  Q_{32} = (1 4 10 11 5)(2 3 8 12 9) |
|  M_{33}={\begin{bmatrix}{\frac {1}{2}}&{\frac {1}{2\phi }}&{\frac {\phi }{2}}\\{\frac {1}{2\phi }}&{\frac {\phi }{2}}&-{\frac {1}{2}}\\-{\frac {\phi }{2}}&{\frac {1}{2}}&{\frac {1}{2\phi }}\end{bmatrix}} |  P_{33} = (1 3 5 2 4) |  Q_{33} = (1 5 9 6 3)(4 7 11 12 8) |
|  M_{34}={\begin{bmatrix}{\frac {1}{2\phi }}&{\frac {\phi }{2}}&{\frac {1}{2}}\\{\frac {\phi }{2}}&-{\frac {1}{2}}&{\frac {1}{2\phi }}\\{\frac {1}{2}}&{\frac {1}{2\phi }}&-{\frac {\phi }{2}}\end{bmatrix}} |  P_{34} = (1 3)(2 5) |  Q_{34} = (1 2)(3 5)(4 9)(6 7)(8 11)(10 12) |
|  M_{35}={\begin{bmatrix}-{\frac {\phi }{2}}&-{\frac {1}{2}}&{\frac {1}{2\phi }}\\{\frac {1}{2}}&-{\frac {1}{2\phi }}&{\frac {\phi }{2}}\\-{\frac {1}{2\phi }}&{\frac {\phi }{2}}&{\frac {1}{2}}\end{bmatrix}} |  P_{35} = (1 3 2 5 4) |  Q_{35} = (1 11 2 7 9)(3 10 6 4 12) |
|  M_{36}={\begin{bmatrix}{\frac {1}{2}}&-{\frac {1}{2\phi }}&-{\frac {\phi }{2}}\\{\frac {1}{2\phi }}&-{\frac {\phi }{2}}&{\frac {1}{2}}\\-{\frac {\phi }{2}}&-{\frac {1}{2}}&-{\frac {1}{2\phi }}\end{bmatrix}} |  P_{36} = (1 3 4 2 5) |  Q_{36} = (1 8 2 4 6)(5 10 9 7 12) |
|  M_{37}={\begin{bmatrix}{\frac {\phi }{2}}&{\frac {1}{2}}&-{\frac {1}{2\phi }}\\-{\frac {1}{2}}&{\frac {1}{2\phi }}&-{\frac {\phi }{2}}\\-{\frac {1}{2\phi }}&{\frac {\phi }{2}}&{\frac {1}{2}}\end{bmatrix}} |  P_{37} = (1 4 5 3 2) |  Q_{37} = (1 2 6 8 4)(5 9 12 10 7) |
|  M_{38}={\begin{bmatrix}0&-1&0\\0&0&-1\\1&0&0\end{bmatrix}} |  P_{38} = (1 4 2) |  Q_{38} = (1 4 7)(2 8 11)(3 10 5)(6 12 9) |
|  M_{39}={\begin{bmatrix}-{\frac {\phi }{2}}&{\frac {1}{2}}&{\frac {1}{2\phi }}\\-{\frac {1}{2}}&-{\frac {1}{2\phi }}&-{\frac {\phi }{2}}\\-{\frac {1}{2\phi }}&-{\frac {\phi }{2}}&{\frac {1}{2}}\end{bmatrix}} |  P_{39} = (1 4 3 5 2) |  Q_{39} = (1 11 4 5 10)(2 12 3 9 8) |
|  M_{40}={\begin{bmatrix}-{\frac {1}{2\phi }}&-{\frac {\phi }{2}}&-{\frac {1}{2}}\\{\frac {\phi }{2}}&-{\frac {1}{2}}&{\frac {1}{2\phi }}\\-{\frac {1}{2}}&-{\frac {1}{2\phi }}&{\frac {\phi }{2}}\end{bmatrix}} |  P_{40} = (1 4 3) |  Q_{40} = (1 10 9)(2 4 12)(3 8 6)(5 7 11) |
|  M_{41}={\begin{bmatrix}0&0&1\\1&0&0\\0&1&0\end{bmatrix}} |  P_{41} = (1 4 5) |  Q_{41} = (1 5 2)(3 7 9)(4 11 6)(8 10 12) |
|  M_{42}={\begin{bmatrix}{\frac {1}{2\phi }}&{\frac {\phi }{2}}&-{\frac {1}{2}}\\{\frac {\phi }{2}}&-{\frac {1}{2}}&-{\frac {1}{2\phi }}\\-{\frac {1}{2}}&-{\frac {1}{2\phi }}&-{\frac {\phi }{2}}\end{bmatrix}} |  P_{42} = (1 4)(3 5) |  Q_{42} = (1 6)(2 3)(4 9)(5 8)(7 12)(10 11) |
|  M_{43}={\begin{bmatrix}-{\frac {\phi }{2}}&{\frac {1}{2}}&-{\frac {1}{2\phi }}\\-{\frac {1}{2}}&-{\frac {1}{2\phi }}&{\frac {\phi }{2}}\\{\frac {1}{2\phi }}&{\frac {\phi }{2}}&{\frac {1}{2}}\end{bmatrix}} |  P_{43} = (1 4 5 2 3) |  Q_{43} = (1 9 7 2 11)(3 12 4 6 10) |
|  M_{44}={\begin{bmatrix}{\frac {1}{2\phi }}&-{\frac {\phi }{2}}&-{\frac {1}{2}}\\-{\frac {\phi }{2}}&-{\frac {1}{2}}&{\frac {1}{2\phi }}\\-{\frac {1}{2}}&{\frac {1}{2\phi }}&-{\frac {\phi }{2}}\end{bmatrix}} |  P_{44} = (1 4)(2 3) |  Q_{44} = (1 8)(2 10)(3 4)(5 12)(6 7)(9 11) |
|  M_{45}={\begin{bmatrix}{\frac {1}{2}}&{\frac {1}{2\phi }}&{\frac {\phi }{2}}\\-{\frac {1}{2\phi }}&-{\frac {\phi }{2}}&{\frac {1}{2}}\\{\frac {\phi }{2}}&-{\frac {1}{2}}&-{\frac {1}{2\phi }}\end{bmatrix}} |  P_{45} = (1 4 2 3 5) |  Q_{45} = (2 7 3 5 4)(6 11 8 9 10) |
|  M_{46}={\begin{bmatrix}{\frac {1}{2}}&{\frac {1}{2\phi }}&-{\frac {\phi }{2}}\\{\frac {1}{2\phi }}&{\frac {\phi }{2}}&{\frac {1}{2}}\\{\frac {\phi }{2}}&-{\frac {1}{2}}&{\frac {1}{2\phi }}\end{bmatrix}} |  P_{46} = (1 4 2 5 3) |  Q_{46} = (1 3 6 9 5)(4 8 12 11 7) |
|  M_{47}={\begin{bmatrix}{\frac {1}{2}}&-{\frac {1}{2\phi }}&{\frac {\phi }{2}}\\-{\frac {1}{2\phi }}&{\frac {\phi }{2}}&{\frac {1}{2}}\\-{\frac {\phi }{2}}&-{\frac {1}{2}}&{\frac {1}{2\phi }}\end{bmatrix}} |  P_{47} = (1 4 3 2 5) |  Q_{47} = (1 7 10 8 3)(2 5 11 12 6) |
|  M_{48}={\begin{bmatrix}-1&0&0\\0&1&0\\0&0&-1\end{bmatrix}} |  P_{48} = (1 4)(2 5) |  Q_{48} = (1 12)(2 9)(3 11)(4 10)(5 6)(7 8) |
|  M_{49}={\begin{bmatrix}-{\frac {1}{2\phi }}&{\frac {\phi }{2}}&{\frac {1}{2}}\\{\frac {\phi }{2}}&{\frac {1}{2}}&-{\frac {1}{2\phi }}\\-{\frac {1}{2}}&{\frac {1}{2\phi }}&-{\frac {\phi }{2}}\end{bmatrix}} |  P_{49} = (1 5 4 3 2) |  Q_{49} = (1 9 3 5 6)(4 11 8 7 12) |
|  M_{50}={\begin{bmatrix}0&0&-1\\1&0&0\\0&-1&0\end{bmatrix}} |  P_{50} = (1 5 2) |  Q_{50} = (1 8 9)(2 3 6)(4 12 5)(7 10 11) |
|  M_{51}={\begin{bmatrix}{\frac {1}{2\phi }}&-{\frac {\phi }{2}}&{\frac {1}{2}}\\{\frac {\phi }{2}}&{\frac {1}{2}}&{\frac {1}{2\phi }}\\-{\frac {1}{2}}&{\frac {1}{2\phi }}&{\frac {\phi }{2}}\end{bmatrix}} |  P_{51} = (1 5 3 4 2) |  Q_{51} = (1 7 11 9 2)(3 4 10 12 6) |
|  M_{52}={\begin{bmatrix}{\frac {\phi }{2}}&-{\frac {1}{2}}&{\frac {1}{2\phi }}\\-{\frac {1}{2}}&-{\frac {1}{2\phi }}&{\frac {\phi }{2}}\\-{\frac {1}{2\phi }}&-{\frac {\phi }{2}}&-{\frac {1}{2}}\end{bmatrix}} |  P_{52} = (1 5 3) |  Q_{52} = (1 4 3)(2 7 8)(5 10 6)(9 11 12) |
|  M_{53}={\begin{bmatrix}0&1&0\\0&0&1\\1&0&0\end{bmatrix}} |  P_{53} = (1 5 4) |  Q_{53} = (1 2 5)(3 9 7)(4 6 11)(8 12 10) |
|  M_{54}={\begin{bmatrix}-{\frac {\phi }{2}}&-{\frac {1}{2}}&-{\frac {1}{2\phi }}\\-{\frac {1}{2}}&{\frac {1}{2\phi }}&{\frac {\phi }{2}}\\-{\frac {1}{2\phi }}&{\frac {\phi }{2}}&-{\frac {1}{2}}\end{bmatrix}} |  P_{54} = (1 5)(3 4) |  Q_{54} = (1 12)(2 11)(3 10)(4 8)(5 9)(6 7) |
|  M_{55}={\begin{bmatrix}{\frac {1}{2\phi }}&{\frac {\phi }{2}}&{\frac {1}{2}}\\-{\frac {\phi }{2}}&{\frac {1}{2}}&-{\frac {1}{2\phi }}\\-{\frac {1}{2}}&-{\frac {1}{2\phi }}&{\frac {\phi }{2}}\end{bmatrix}} |  P_{55} = (1 5 4 2 3) |  Q_{55} = (1 5 11 10 4)(2 9 12 8 3) |