Stir the sugar into the water. Sprinkle in the yeast. Let the mixture stand until the yeast bubbles to the surface. Stir in the white flour and 1/2 whole wheat flour. Mix well. Cover the batter with waxed paper and a towel. Let it sit until it is bubbly, 30 minutes to 1 hour.
Stir down the batter, and add the salt, the rye flour and the corn flour.
Spread the remaining 1/2 cup of whole wheat flour over a work surface, and turn the dough onto it. Knead the wheat flour into the dough, sprinkling with more white flour if the dough is still too sticky. Knead until the dough is firm but springy.
Grease a clean bowl with the vegetable oil. Set the dough in the bowl, and turn the dough over to coat it completely with the oil.
Cover the dough with waxed paper and a towel, and set it to rise until it is double in bulk, about 1 hour, or overnight in the refridgerator.
Preheat oven to 375 degrees.
Punch down the dough, and divide in two. Knead it into two round loaves. With a sharp knife, cut a slash around the circumference of each loaf and prick the top. Set the loaves on a lightly floured cookie sheet. The dough need not rise again for baking.
Bake the bread for 45 minutes, or until a tap on the bottom of the loaf produces a hollow sound. Set the loaves on racks to cool.