2
$\begingroup$

I am trying to draw a shape which has only 5 symmetries

I know Square has 8

Rectangle/parallelogram has 4

Triangle has 6

Circle has infinite

how do i know which shape has only 5

I know that a regular polygon with $n$ sides has $2n$ symmetries so there is no regular polygon with order of symmetry 5

so i came up with this one which has only rotational symmetry and order 5 enter image description here

my question is are there any shapes with symmetries of order 5 and which are not entirely rotational symmetries

also how do i generally find them for a given an odd order?

Thanks for any help.

$\endgroup$
3
$\begingroup$

Note that any reflection has order $2$, so any group of symmetries which includes a reflection must have even order.

You can generalise your solution for $5$ to any odd order.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.