The mathematical model for the fourth dimension is the tesseract, two connected parallel cubes that form a hypercube. The volume of the tesseract equals a side of a cube to the fourth power. McCaulay's Fourth Dimension Mathematics introduces a new mathematical model for the fourth dimension that turns the tesseract inside-out to form a six-rayed star, or hexact. The hexact is six square pyramids around a cube to form a 24-sided polyhedron. This publication includes details on the derivation of the formulas for the height, volume, and surface area of a hexact. The concepts are shown as linear equations, graphs, and tables, along with specific examples. The fourth dimension mathematics model is extended to the fifth and sixth dimensions.