Article · Wikipedia archive · Last revised Jul 18, 2026

Crumpled cube

In geometric topology, a branch of mathematics, a crumpled cube is any space in R3 homeomorphic to a 2-sphere together with its interior. Lininger showed in 1965 that the union of a crumpled cube and an open 3-ball glued along their boundaries is a 3-sphere.

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Jul 18, 2026

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In geometric topology, a branch of mathematics, a crumpled cube is any space in R³ homeomorphic to a 2-sphere together with its interior.¹ Lininger showed in 1965 that the union of a crumpled cube and an open 3-ball glued along their boundaries is a 3-sphere.²

References

References

Martin, Joseph (1966). "The sum of two crumpled cubes". Michigan Mathematical Journal. 13 (2): 147–151. doi:10.1307/mmj/1028999538.
Lininger, Lloyd L. (1965). "Some results on crumpled cubes". Transactions of the American Mathematical Society. 118: 534–549. doi:10.2307/1993977. ISSN 0002-9947. JSTOR 1993977. MR 0178460.