Measured across the flats, a 1-inch hexagon is larger than a 1-inch square. To use a table saw, you'll need wider material. Set the blade height at less than mid-thickness to preserve the far face, and set the fence against the near face for cutting the far bevel, at a precise distance. Cut the 4 bevel faces by flipping and reversing. Remove the mid-thickness material by whatever means, and plane the corners flush. Use a draftsman's 30-60 triangle to set the bevel angle (more reliable than the saw's gauge); put some masking tape on 2 edges to mark the blade height and the offset from the fence. If you don't have a zero-clearance insert, use a sled; AND USE A PUSH STICK.
Lathe with index wheel, and a router sled, is probably less bother. At best, from 1-inch square stock, the result will be a hexagon 1-inch across the points, not the flats; and cut all 6 faces.