Puzzling the 120-Cell

The puzzling role of TRAIL in endothelial cell biology.

Cell Biology To the Editor: In their study published online in Arteriosclerosis, Thrombosis, and Vascular Biology, O’Brien et al demonstrate that activated protein C (APC) decreases tumor necrosis factor (TNF)-related apoptosis-inducing ligand (TRAIL) expression in endothelial cells.1 Although the molecular mechanism by which APC decreases the expression of TRAIL mRNA and protein via an Egr-1/E...

Small Covers of the Dodecahedron and the 120-cell

Let P be the right-angled hyperbolic dodecahedron or 120-cell, and let W be the group generated by reflections across codimension-one faces of P . We prove that if Γ ⊂ W is a torsion free subgroup of minimal index, then the corresponding hyperbolic manifold Hn/Γ is determined up to homeomorphism by Γ modulo the symmetry group of P .

The skeleton of the 120-cell is not 5-gonal

The Story of the 120-Cell, Volume 48, Number 1

O ne of the most beautiful objects in mathematics is the regular polytope in R4 whose boundary consists of 120 dodecahedral cells. This 120-cell is a rarity among rarities because it lives in three very special worlds. Its home is among the regular polytopes in R4, but it also lives in the remarkable sphere S3 and in the quaternions H. And if this is not enough, the 120-cell encodes the symmetr...

Puzzling Permutations

We show how to describe and analyse multistage interconnection networks in a relational framework. We give simple elegant descriptions of butterfly networks, using only two functions for building networks from smaller networks. By studying the algebra of these functions, we can give a clear account of the properties of networks, without resorting to the standard methods of reasoning in terms of...