Thorold Gosset discovered the semiregular 4-polytopes, including the snub 24-cell with 96 vertices, which falls between the 24-cell and the 600-cell in the sequence of convex 4-polytopes of increasing size and complexity in the same radius. Gosset's construction of the 600-cell from the 24-cell is in two steps, using the snub 24-cell as an intermediate form. In the first, more complex step (described elsewhere) the snub 24-cell is constructed by a special snub truncation of a 24-cell at the golden sections of its edges. In the second step the 600-cell is constructed in a straightforward manner by adding 4-pyramids (vertices) to facets of the snub 24-cell.