I was interested in finding a pattern for finding out the no . of isometrics of regular polygons. Like a tetrahedron has 12 no. Of isometrics as being isomorphic to alternating group 4 . similarly what would be the isometrics of a cube ,a regular cylinder , cuboid , cone ,pyramid. And which group are they isomorphic to?. Can anyone give a pattern or formula to determine the no. Of isometrics based on any criterion?
how do we determine the isometrics of a regular polygon?
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group-isomorphism
1 Answers
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For rectangle ,rhombus,space cube ,swastika of n arms the no. A of isometrics are 4,4,48 and n!.