the convex hull of 5 disjoint (120-point) 600-cells. Each (120-point) 600-cell is the convex hull of 5 disjoint (24-point) 24-cells, so the 120-cell is the convex hull of 25 disjoint 24-cells. Each 24-cell is the convex hull of 3 disjoint (8-point) 16-cells, so the 120-cell is the convex hull of 75 disjoint 16-cells. Uniquely, the (600-point) 120-cell is the convex hull of 120 disjoint (5-point) 5-cells. Polyhedral graph Considering the adjacency matrix of the vertices representing its polyhedral graph, the graph diameter is 15, connecting each vertex to its coordinate-negation, at a Euclidean distance of 4 away (its circumdiameter), and there are 24 different paths to connect them along the polytope edges. From each vertex, there are 4 vertices at distance 1, 12 at distance 2, 24 at distance 3, 36 at distance 4, 52 at distance 5, 68 at distance 6, 76 at distance 7, 78 at distance 8, 72 at distance 9, 64 at distance 10, 56 at distance 11, 40 at distance 12, 12 at distance 13, 4 at distance 14, and 1 at distance 15. The adjacency matrix has 27 distinct eigenvalues ranging from , with a multiplicity of 4, to 4, with a multiplicity of 1. The multiplicity of eigenvalue 0 is 18, and the rank of the adjacency matrix is 582. The vertices of the 120-cell polyhedral graph are 3-colorable. It has not been published whether the graph is Hamiltonian. It is Eulerian having degree 4 in every vertex. Concentric hulls Constructions The 120-cell is the sixth in the sequence of 6 convex regular 4-polytopes (in order of size and complexity). It can be deconstructed into ten distinct instances (or five disjoint instances) of its immediate predecessor (and dual) the 600-cell, just as the 600-cell can be deconstructed into twenty-five distinct instances (or five disjoint instances) of its immediate predecessor the 24-cell, the 24-cell can be deconstructed into three distinct instances of its predecessor the tesseract (8-cell), and the 8-cell can be deconstructed into two disjoint instances of its predecessor the 16-cell. The 120-cell contains 675 distinct instances (75 disjoint instances) of the 16-cell. The reverse procedure to construct each of these from an instance of its predecessor preserves the radius of the predecessor, but generally produces a successor with a smaller edge length. The 600-cell's edge length is ~0.618 times its radius (the inverse golden ratio), but the 120-cell's edge length is ~0.270