Examples
The polar body of an n-dimensional unit sphere is itself another unit sphere. Thus, its Mahler volume is just the square of its volume,
Here Γ represents the Gamma function. By affine invariance, any ellipsoid has the same Mahler volume.
The polar body of a polyhedron or polytope is its dual polyhedron or dual polytope. In particular, the polar body of a cube or hypercube is an octahedron or cross polytope. Its Mahler volume can be calculated as
The Mahler volume of the sphere is larger than the Mahler volume of the hypercube by a factor of approximately .
Read more about this topic: Mahler Volume
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