**1.**

Cube is the only regular hexahedron and is one of the five Platonic solids.

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Cube is the only regular hexahedron and is one of the five Platonic solids.

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Cube is a square parallelepiped, an equilateral cuboid and a right rhombohedron a 3-zonohedron.

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Cube is the only convex polyhedron whose faces are all squares.

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Cube has four special orthogonal projections, centered, on a vertex, edges, face and normal to its vertex figure.

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Cube can be represented as a spherical tiling, and projected onto the plane via a stereographic projection.

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Cube can be considered the limiting case of a 3D superellipsoid as all three exponents approach infinity.

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Cube has the largest volume among cuboids with a given surface area.

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Cube has three uniform colorings, named by the colors of the square faces around each vertex: 111, 112, 123.

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Cube has four classes of symmetry, which can be represented by vertex-transitive coloring the faces.

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Cube has eleven nets: that is, there are eleven ways to flatten a hollow cube by cutting seven edges.

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Cube is the cell of the only regular tiling of three-dimensional Euclidean space.

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Cube is a special case in various classes of general polyhedra:.

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Cube is topologically related to a series of spherical polyhedral and tilings with order-3 vertex figures.

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Cube is topologically related as a part of sequence of regular tilings, extending into the hyperbolic plane: {4, p}, p=3, 4, 5.

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Cube is a part of a sequence of rhombic polyhedra and tilings with [n, 3] Coxeter group symmetry.

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