# Singular

#### D.13.2.44 maximalFace

Procedure from library `polymake.lib` (see polymake_lib).

Usage:
maximalFace(p,v); p polytope, v intvec

Assume:
v lies in the negative dual tail cone of p

Return:
intmat, vertices of the face of p on which the linear form v is maximal

Note:
the maximal face is independent of the first coordinate of v since p is considered as a polytope in the plane (first coordinate) = 1.

Example:
 ```LIB "polymake.lib"; ==> Welcome to polymake version ==> Copyright (c) 1997-2015 ==> Ewgenij Gawrilow, Michael Joswig (TU Darmstadt) ==> http://www.polymake.org intmat M[3][3]= 1,1,0, 1,0,1, 1,-1,-1; intvec v = 0,1,1; polytope p = polytopeViaPoints(M); maximalFace(p,v); ==> polymake: used package cdd ==> cddlib ==> Implementation of the double description method of Motzkin et al. ==> Copyright by Komei Fukuda. ==> http://www.ifor.math.ethz.ch/~fukuda/cdd_home/cdd.html ==> ==> polymake: used package ppl ==> The Parma Polyhedra Library (PPL): A C++ library for convex polyhedra ==> and other numerical abstractions. ==> http://www.cs.unipr.it/ppl/ ==> ==> 1,1,0, ==> 1,0,1 intvec w = -5,1,1; maximalFace(p,w); ==> 1,1,0, ==> 1,0,1 ```