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  2. Rubik's family cubes of varying sizes - Wikipedia

    en.wikipedia.org/wiki/Rubik's_family_cubes_of...

    A cube is solvable if the set state has existed some time in the past and if no tampering of the cube has occurred (e.g. by rearrangement of stickers on hardware cubes or by doing the equivalent on software cubes). Rules for the standard size 3 Rubik's cube [3] [4] and for the complete Rubik's cube family [5] have been documented. Those rules ...

  3. Cubical complex - Wikipedia

    en.wikipedia.org/wiki/Cubical_complex

    Equivalently, an elementary cube is any translate of a unit cube [,] embedded in Euclidean space (for some , {} with ). [3] A set X ⊆ R d {\displaystyle X\subseteq \mathbf {R} ^{d}} is a cubical complex (or cubical set ) if it can be written as a union of elementary cubes (or possibly, is homeomorphic to such a set).

  4. Solid geometry - Wikipedia

    en.wikipedia.org/wiki/Solid_geometry

    A solid figure is the region of 3D space bounded by a two-dimensional closed surface; for example, a solid ball consists of a sphere and its interior. Solid geometry deals with the measurements of volumes of various solids, including pyramids , prisms (and other polyhedrons ), cubes , cylinders , cones (and truncated cones ).

  5. Point groups in three dimensions - Wikipedia

    en.wikipedia.org/wiki/Point_groups_in_three...

    When comparing the symmetry type of two objects, the origin is chosen for each separately, i.e., they need not have the same center. Moreover, two objects are considered to be of the same symmetry type if their symmetry groups are conjugate subgroups of O(3) (two subgroups H 1, H 2 of a group G are conjugate, if there exists g ∈ G such that H 1 = g −1 H 2 g).

  6. Three-dimensional space - Wikipedia

    en.wikipedia.org/wiki/Three-dimensional_space

    A representation of a three-dimensional Cartesian coordinate system. In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (coordinates) are required to determine the position of a point.

  7. Cube - Wikipedia

    en.wikipedia.org/wiki/Cube

    3D model of a cube. The cube is a special case among every cuboids. As mentioned above, the cube can be represented as the rectangular cuboid with edges equal in length and all of its faces are all squares. [1] The cube may be considered as the parallelepiped in which all of its edges are equal edges. [20]

  8. Manipulative (mathematics education) - Wikipedia

    en.wikipedia.org/wiki/Manipulative_(mathematics...

    Cuisenaire rods in a staircase arrangement Interlocking "multilink" linking cubes A Polydron icosahedron. In mathematics education, a manipulative is an object which is designed so that a learner can perceive some mathematical concept by manipulating it, hence its name.

  9. 3-manifold - Wikipedia

    en.wikipedia.org/wiki/3-manifold

    That is, the 3-torus is R 3 modulo the action of the integer lattice Z 3 (with the action being taken as vector addition). Equivalently, the 3-torus is obtained from the 3-dimensional cube by gluing the opposite faces together. A 3-torus in this sense is an example of a 3-dimensional compact manifold. It is also an example of a compact abelian ...