Spherical symmetry patterns

Contents

(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:

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