isFano X
A normal toric variety is Fano if its anticanonical divisor, namely the sum of all the torus-invariant irreducible divisors, is ample. This is equivalent to saying that the polyhedron associated to the anticanonical divisor is a reflexive polytope.
Projective space is Fano.
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There are eighteen smooth Fano toric threefolds.
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There are also many singular Fano toric varieties.
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To avoid duplicate computations, the attribute is cached in the normal toric variety.