What you know is wrong: it actually takes fewer muscles to frown than to smile.
It takes 12 muscles to smile and 11 muscles to frown.
Muscles involved in a "zygomatic" (i.e., genuine) smile:
Zygomaticus major and minor. These muscles pull up the corners of the mouth. They're bilateral (one set on either side of the face). Total number of muscles: 4.
Orbicularis oculi. One of these muscles encircles each eye and causes crinkling. Total: 2.
Levator labii superioris. Pulls up corner of lip and nose. Bilateral. Total: 2.
Levator anguli oris. Also helps elevate angle of mouth. Bilateral. Total: 2.
Risorius. Pulls corner of mouth to the side. Bilateral. Total: 2. Grand total for smiling: 12.
Principal muscles involved in a frown:
Orbicularis oculi (again). Total: 2.
Platysma. Pulls down lips and wrinkles skin of lower face. Bilateral (though joined at midline). Total: 2.
Corrugator supercilii (bilateral) and procerus (unilateral). Furrow brow. Total: 3.
Orbicularis oris. Encircles mouth; purses lips. Unilateral. Total: 1.
Mentalis. Depresses lower lip. Unilateral. Total: 1.
Depressor anguli oris. Pulls corner of mouth down. Bilateral. Total: 2. Grand total for frowning: 11.