Tesselation of a triangle by repeated barycentric subdivision.
The isogonal sponges on the cubic lattice.
The alternating sign matrix polytope.
The angle defect for arbitrary polyhedra.
The Bellows conjecture.
The Cayley Trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings
In 1994, Sturmfels gave a polyhedral version of the Cayley Trick of elimination theory: he established an order-preserving bijection between the posets of coherent mixed subdivisions of a Minkowski sum of point configurations and of coherent polyhedral subdivisions of the associated Cayley embedding . In this paper we extend this correspondence in a natural way to cover also non-coherent subdivisions. As an application, we show that the Cayley Trick combined with results of Santos on subdivisions...
The Cayley–Menger determinant is irreducible for .
The cd-index of Bruhat intervals.
The centers of gravity of the associahedron and of the permutahedron are the same.
The Classification of Quasi-Regular Polyhedra of Genus 2.
The combinatorially regular polyhedra of index 2.
The Cubical d-Polytopes with Fewer than 2d+1 Vertices.
The cyclic sieving phenomenon for faces of cyclic polytopes.
The dissection of five-dimensional simplices into orthoschemes.
The edge-minimal polyhedral maps of Euler characteristic .
The Ehrhart polynomial of a lattice -simplex.
The generalized Baues problem for cyclic polytopes. II.
The -vector of a Gorenstein toric ring of a compressed polytope.
The hypermetric cone on seven vertices.
The largest intersection lattice of a discriminantal arrangement.