SYNOPSIS

poly.x [-<Option-string>] [in-file [out-file]]

DESCRIPTION

Computes data of a polytope P

The poly-<num>d.x variant programs, where <num> is one of 4, 5, 6 and 11 work in different dimensions ; poly.x defaults to dimension 6.

Options (concatenate any number of them into <Option-string>):

h print this information

  • f use as filter

  • g general output ; for P reflexive: numbers of (dual) points/vertices, Hodge numbers and if P is not reflexive: numbers of points, vertices, equations

p points of P

  • v vertices of P

  • e equations of P/vertices of P-dual

  • m pairing matrix between vertices and equations

  • d points of P-dual (only if P reflexive)

  • a all of the above except h,f

  • l LG-`Hodge numbers' from single weight input

  • r ignore non-reflexive input

  • D dual polytope as input (ref only)

  • n do not complete polytope or calculate Hodge numbers

  • i incidence information

  • s check for span property (only if P from CWS)

  • I check for IP property

  • S number of symmetries

  • T upper triangular form

  • N normal form

  • t traced normal form computation

  • V IP simplices among vertices of P*

  • P IP simplices among points of P* (with 1<=codim<=# when # is set)

  • Z lattice quotients for IP simplices

  • # #=1,2,3 fibers spanned by IP simplices with codim<=#

  • ## ##=11,22,33,(12,23): all (fibered) fibers with specified codim(s) when combined: ### = (##)#

  • A affine normal form

  • B Barycenter and lattice volume [# ... points at deg #]

  • F print all facets

  • G Gorenstein: divisible by I>1

  • L like 'l' with Hodge data for twisted sectors

  • U simplicial facets in N-lattice

  • U1 Fano (simplicial and unimodular facets in N-lattice)

  • U5 5d fano from reflexive 4d projections (M lattice)

  • C1 conifold CY (unimodular or square 2-faces)

  • C2 conifold FANO (divisible by 2 & basic 2 faces)

  • E symmetries related to Einstein-Kaehler Metrics

Input

degrees and weights `d1 w11 w12 ... d2 w21 w22 ...' or `d np' or `np d' (d=Dimension, np=#[points]) and (after newline) np*d coordinates

Output

as specified by options

RELATED TO poly-11d.x…

A complete manual is available here : http://arxiv.org/abs/1205.4147