Step 1: Understanding floral organization.
Trimerous flowers have floral parts in multiples of three, and tricyclic flowers have three distinct whorls (calyx, corolla, androecium). These features are typical of monocotyledons.
Step 2: Analysis of Allium.
Allium is a monocot, but its floral organization does not strictly represent the trimerous and tricyclic condition in the context asked. Hence, it is not the best match.
Step 3: Analysis of Asparagus.
Asparagus shows modified floral structures but does not represent clearly trimerous and tricyclic complete floral arrangement.
Step 4: Analysis of Smilax.
Smilax is a monocot plant that shows trimerous floral symmetry and typically exhibits a tricyclic arrangement, making it the correct example.
Step 5: Analysis of male flowers of Smilax.
Although Smilax male flowers also show monocot features, the general correct identification is Smilax as a whole.
Step 6: Final conclusion.
Thus, Smilax is the correct example of trimerous and tricyclic flowers.
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\boxed{(3)}
\]