# poly-4d.x - Man Page

manual page for poly-4d.x 2.11

## Synopsis

**poly-4d.x** [*-<Option-string>*] [*in-file* [*out-file*]]

## Description

This is 'bin/poly-4d.x': computing data of a polytope P

Options (concatenate any number of them into <Option-string>): h print this information f use as filter g general output:

P reflexive: numbers of (dual) points/vertices, Hodge numbers P 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