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After reading some of "The Symmetries of Things", I've tried to look if Im understanding the concept correctly... I'm trying to calculate the next picture symetric: enter image description here

Each triangle gives us $$`*`$$ since its kleidoscopes. Also we have wanderings, so I get also $$`o`$$

A total score of $$*o$$ which is equal to $$ 3$ $$ According to the magic thorem...which means I have a mistake(since it cant get more then 2$ of symmetrics...)

Please help me to find where am I wrong?

references: https://www.crcpress.com/The-Symmetries-of-Things/Conway-Burgiel-Goodman-Strauss/p/book/9781568812205#googlePreviewContainer (You can read all what im asking on the preview section).

http://blog.kleinproject.org/?p=1381

Edit:

Another option i found(not sure about it), maybe its not wanderings instead its a miracle which gives us the score $$x$$ A total of $$*x$$ score which is then $$ 2$ $$ and could be correct according to the magic thorem.

enter image description here

thanks!

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    Have you seen (https://en.wikipedia.org/wiki/Wallpaper_group) and (https://commons.wikimedia.org/wiki/Wallpaper_group_diagrams) ? – 2017-01-30
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    @JeanMarie I did not , thanks! – 2017-01-31

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A solution was found, Since it has 45,45,90 degrees and reflection, score is *442 (reflection+pi/4+pi/4+pi/2) which is equal to 1$+3/8$+3/8$+1/4$=2$ Correct by the magic thorem. thanks everyone!