Actually, the space-time is four-dimensional, but here is showed two-dimensional space-time by reducing space to one dimension for simplicity. When the space is assumed as two dimensions, the space-time graph becomes a three-dimensional shape which has a curved surface boundary which is made by revolution of the world line of the light around the vertical axis. This curved surface is a shape that is like two cones standing opposite to each other in top and bottom. These cones are called a Light Cone.
It is impossible for us to draw the actual four-dimensional spase-time which has three-dimensional space. We cannot handle it by not less than mathematical formal method. In the 4-D world, the circle (oval) of "the section" of the Light Cone is equivalent in the spherical surface (spheroid surface) of the Light Cone as super-solid.
But, what is showed here is only reduced two-dimensional space-time diagram.