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The deltoid (top left) was
studied by lightweights like
Euler and Steiner. Its perimeter
is 16/3 of the radius; while its
area is 2/9 pi times the radius
squared. The astroid (middle left)
has a perimeter of 6 times the
radius and an area of 3/8 pi times
the radius squared. As they say
on Criminal Minds - there is a
pattern here.