convex optimization – Can a 3D polyhedron have both v-representation and h-representation(constraints) in its definition?

i plan to use this polyhedra class which i am writing for spatial optimization,

function NDConvexPart2(v::Array)
hull = spatial.ConvexHull(v)
equations = hull.equations
shape = size(v)
m = shape(1)
n = shape(2)
equationsm = size(equations)(1)
p = Variable(shape)
print(m,n)
v = sort(v, dims = n -1)
A = ones(shape)
x = Variable(m)
y = Variable(m)

λ = Variable(shape)
c = 0
# Hyperplanes 
for i in 1:length(equationm)
    add_constraint!(x, x(i+1) -x(i) == d(i))
end

# convex combination 
for i in 1:m
     c = c + λ(i) * v(i)
end  
add_constraint!(p,c <= sum(x))
add_constraint!(λ,λ >= 0)
add_constraint!(λ,λ <= 1)
add_constraint!(λ, sum(λ) == 1)
return x

end

1.i need the hyperplanes (h-representations) to maintain the distance between the points, i am using equations of the convex hull to build the h-representation – is this right?
2.i need v-rep to keep the set convex(do i need this really? because i am using the hull vertices, need advice