In a large bowl, dissolve yeast in warm water. Add sugar, oil, eggs, salt and 3 cups all-purpose flour. Beat on medium speed for 3 minutes. Divide dough into three portions; place in separate bowls. Add remaining all-purpose flour to one bowl, whole wheat flour to another bowl and the cornmeal to last bowl.
Turn each portion onto a floured surface; knead until smooth and elastic, about 6-8 minutes. Place each portion in a greased bowl, turning once to grease the top. Cover and let rise in a warm place until doubled, about 1 hour.
Divide each portion of dough into 24 pieces. Shape each into a ball. Place one of each of the balls in greased muffin cups; brush with butter. Cover and let rise until doubled, about 30 minutes.
Preheat oven to 375°. Bake 15-18 minutes or until golden brown. Remove from pans to wire racks.Yield: 2 dozen.