using Polyhedra
h = HalfSpace([2, 1], 1) ∩ HalfSpace([2, -1], 1) ∩ HalfSpace([-1, 2], 1) ∩ HalfSpace([-1, -2], 1)

using GLPK
using JuMP
cheby_center, cheby_radius = chebyshevcenter(h, GLPK.Optimizer)

using Plots

plot(polyhedron(h), axis_ratio=:equal)
α = range(0, stop=2π, length=100)
x = cheby_center[1] .+ cheby_radius .* cos.(α)
y = cheby_center[2] .+ cheby_radius .* sin.(α)
plot!(x, y, linewidth=4)
scatter!([cheby_center[1]], [cheby_center[2]])