Union of 2 solid tori (S¹ × S²)

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There are different ways of gluing solid tori along their boundaries, resulting in different manifolds (most common are S¹ × S² and S³). This video presents 2 ways to visualize S¹ × S² as the union of 2 solid toruses. One of them uses Heegaard splitting, which can be useful when studying 3-manifolds.
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What software do you use to make these animations?

amandeep
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Does it visulaise S^3 as union of 2 solid torus?

yashica