# isNormal(Polyhedron) -- checks if a polytope is normal in the ambient lattice

## Synopsis

• Function: isNormal
• Usage:
b = isNormal P
• Inputs:
• P, , which must be compact
• Outputs:
• b, , true if P is normal in the ambient lattice

## Description

isNormal can only be applied to polytopes, i.e. compact polyhedra. It embeds the polytope on height 1 in a space of dimension plus 1 and takes the Cone over this polytope. Then it checks if all elements of the Hilbert basis lie in height 1.

 i1 : P = convexHull transpose matrix {{0,0,0},{1,0,0},{0,1,0},{1,1,3}} o1 = {ambient dimension => 3 } dimension of lineality space => 0 dimension of polyhedron => 3 number of facets => 4 number of rays => 0 number of vertices => 4 o1 : Polyhedron i2 : isNormal P o2 = false