The dodecic surface defined by
(1)

where
(2)
 
(3)
 
(4)
 
(5)
 
(6)
 
(7)
 
(8)
 
(9)
 
(10)
 
(11)
 
(12)
 
(13)
 
(14)
 
(15)
 
(16)

and are both invariants of order 12. It was discovered by A. Sarti in 1999.
The version with arbitrary and has exactly 600 ordinary points (Endraß), and taking gives the surface with 560 real ordinary points illustrated above.
The Sarti surface is invariant under the bipolyhedral group.