Editing Cube (section)

=== Miscellaneous ===
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 | image1 = UC07-6 cubes.png
 | image2 = UC08-3 cubes.png
 | image3 = UC09-5 cubes.png
 | footer = Enumeration according to {{harvtxt|Skilling|1976}}: compound of six cubes with rotational freedom <math> \mathrm{UC}_7 </math>, [[Compound of three cubes|three cubes]] <math> \mathrm{UC}_8 </math>, and [[Compound of five cubes|five cubes]] <math> \mathrm{UC}_9 </math>
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{{anchor|Compound of cubes}}Compound of cubes is the [[polyhedral compound]]s in which the cubes share the same centre. They belong to the [[uniform polyhedron compound]], meaning they are polyhedral compounds whose constituents are identical (although possibly [[enantiomorphous]]) [[uniform polyhedra]], in an arrangement that is also uniform. Respectively, the list of compounds enumerated by {{harvtxt|Skilling|1976}} in the seventh to ninth uniform compounds for the compound of six cubes with rotational freedom, [[Compound of three cubes|three cubes]], and five cubes.{{r|skilling}} Two compounds, consisting of [[compound of two cubes|two]] and three cubes were found in [[M. C. Escher|Escher]]'s [[wood engraving]] print [[Stars (M. C. Escher)|''Stars'']] and [[Max Brückner]]'s book ''Vielecke und Vielflache''.{{r|hart}}

{{multiple image
 | image1 = Square on sphere.svg
 | caption1 = Spherical cube
 | image2 = 3-Manifold 3-Torus.png
 | caption2 = A view in [[3-torus|three-dimensional torus]]
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}}
{{anchor|Spherical cube}}The spherical cube represents the [[spherical polyhedron]], which can be modeled by the [[Arc (geometry)|arc]] of [[great circle]]s, creating bounds as the edges of a [[spherical polygon|spherical square]].{{r|yackel}}
Hence, the spherical cube consists of six spherical squares with 120° interior angles on each vertex. It has [[vector equilibrium]], meaning that the distance from the centroid and each vertex is the same as the distance from that and each edge.{{r|popko|fuller}} Its dual is the [[spherical octahedron]].{{r|yackel}}

The topological object [[3-torus|three-dimensional torus]] is a topological space defined to be [[homeomorphic]] to the Cartesian product of three circles. It can be represented as a three-dimensional model of the cube shape.{{r|marar}}