  Computing the isotopy type of a hypersurface, defined as the positive real
zero set of a multivariate polynomial, is a challenging problem in real
algebraic geometry. We focus on the case where the defining polynomial has
combinatorially restricted exponent vectors and fixed coefficient signs,
enabling faster computation of the isotopy type. In particular, Viro's
patchworking provides a polyhedral complex that has the same isotopy type as
the hypersurface, for certain choices of the coefficients. So we present
properties of the signed support, focussing mainly on the case of n-variate
(n+3)-nomials, that ensure all possible isotopy types can be obtained via
patchworking. To prove this, we study the signed reduced A-discriminant and
show that it has a simple structure if the signed support satisfies some
combinatorial conditions.
