The standard topological $n$-cube is the space $[0,1]^n$, where $[0,1]$ is the unit interval. The collection of topological cubes forms a topological cocubical set?.

Felix Klein, chapter I.5 of Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen vom fünften Grade, 1884, translated as Lectures on the Icosahedron and the Resolution of Equations of Degree Five by George Morrice 1888, online version

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