Xmas Greetings from Elefsina

On the twelfth day of Xmas, my true love gave 2 me
Twelve perfect numbers,
Eleven loops a-leaping,
Ten tangents touching, 
Nine diameters,
Eight hypercubes,
Seven spirals spinning,
Six Cantor’s circles,
FIVE MATH RINGS,
Four fractal sets,
three dragon curves,
two square roots and an Axiom of geometry!