Icon wrote:Is that a 24cell? It dosen't look like it. And also, is a 24cell a four dimensional object?
That is the projection of the 24-cell, a 4D object, into 3D space. The 24-cell is composed of 24 octahedra folded together in 4D space. In the process of projection, facets of the 24-cell that are obscured to the 4D viewer are culled, so only 6 of the 24 cells are actually visible in the image. This is similar to how, if you look at one of the corners of a cube, you can only see 3 of the 6 faces, because the other 3 faces are obscured behind these 3 faces. Only 6 of the 24 cells are visible to the 4D viewer, because they are "facing" him, whereas the others are behind the 6 cells.
If you look carefully at the image, you will see that it is composed of 6 (slightly flattened) octahedra meeting at the center of the image. These octahedra look flattened because they are slightly bent into the 4th direction, just like how if you look at a square from an angle, it looks like a trapezoid. The octahedra are joined to each other via their triangular faces. Only some of these connections are shown, since the rest of the faces are hidden. They are joined at the "outer" faces of the image.
(Think about looking at the corner of a cube: the image is a hexagon of some sort, with three of the visible faces laid out in the hexagon. The outer edges of the hexagon are where the visible faces are connected to the hidden faces. The analogous 4D->3D situation is similar: the outer faces of the image are where the visible cells are joined to the hidden cells.)