Spherical symmetry patterns

(This is a work in progess...) 

The Four Fundamental Features

  • wonders:  repeated without reflection. not explained by gyrations, mirrors or miracles
  • gyrations: rotational symmetry
  • kaleidoscopes:  mirror lines
  • miracles: mirrorless crossing

Conway Cost$

\large\color{blue}{\bf{\circ}}: 2
\large\color{blue}{\bf{N}}: \frac{N-1}{N}
\large\color{blue}{\bf{\infty}}: 1
\large\color{red}{\bf{\ast}}: 1
\large\color{red}{\bf{\times}}: 1
\large\color{red}{\bf{N}}: \frac{N-1}{2N}
\large\color{red}{\bf{\infty}}: \frac{1}{2}

Total cost of a spherical  symmetry pattern is less than 2

14 spherical symmetry possibilities:

                                       \large \begin{array}{cccccc}\color{red}{*532}&\color{red}{*432}&\color{red}{*332}&\color{red}{*22N}&\color{red}{*NN}\\&&&&\color{blue}{N}\color{red}{*}\\&&\color{blue}{3}\color{red}{*2}&\color{blue}{2}\color{red}{*N}&\\&&&&\color{blue}{N}\color{red}{\times}\\\color{blue}{532}&\color{blue}{432}&\color{blue}{332}&\color{blue}{22N}&\color{blue}{NN}\end{array}

\color{red}{*532}

\color{red}{*432}

\color{red}{*332}

\color{red}{*22N}

\color{red}{*NN}

\color{blue}{3}\color{red}{*2}

\color{blue}{2}\color{red}{*N}

\color{blue}{N}\color{red}{*}

\color{blue}{N}\color{red}{\times}

\color{blue}{532}

\color{blue}{432}

\color{blue}{332}

\color{blue}{22N}

\color{blue}{NN}

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