Displaying similar documents to “Viro's theorem for complete intersections”

On the refinements of a polyhedral subdivision.

Francisco Santos (2001)

Collectanea Mathematica

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Let pi: P --> Q be an affine projection map between two polytopes P and Q. Billera and Sturmfels introduced in 1992 the concept of polyhedral subdivisions of Q induced by pi (or pi-induced) and the fiber polytope of the projection: a polytope Sygma(P,pi) of dimension dim(P)-dim(Q) whose faces are in correspondence with the coherent pi-induced subdivisions (or pi-coherent subdivisions). In this paper we investigate the structure of the poset of pi-induced refinements of a pi-induced...

Gosset polytopes in integral octonions

Woo-Nyoung Chang, Jae-Hyouk Lee, Sung Hwan Lee, Young Jun Lee (2014)

Czechoslovak Mathematical Journal

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We study the integral quaternions and the integral octonions along the combinatorics of the 24 -cell, a uniform polytope with the symmetry D 4 , and the Gosset polytope 4 21 with the symmetry E 8 . We identify the set of the unit integral octonions or quaternions as a Gosset polytope 4 21 or a 24 -cell and describe the subsets of integral numbers having small length as certain combinations of unit integral numbers according to the E 8 or D 4 actions on the 4 21 or the 24 -cell, respectively. Moreover, we show...