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  2. 3-fold - Wikipedia

    en.wikipedia.org/wiki/3-fold

    In algebraic geometry, a 3-fold or threefold is a 3-dimensional algebraic variety. The Mori program showed that 3-folds have minimal models. References

  3. Rotational symmetry - Wikipedia

    en.wikipedia.org/wiki/Rotational_symmetry

    Therefore, the number of 2-, 3-, 4-, and 6-fold rotocenters per primitive cell is 4, 3, 2, and 1, respectively, again including 4-fold as a special case of 2-fold, etc. 3-fold rotational symmetry at one point and 2-fold at another one (or ditto in 3D with respect to parallel axes) implies rotation group p6, i.e. double translational symmetry ...

  4. Point groups in three dimensions - Wikipedia

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

    The three-fold axes give rise to four D 3d subgroups. The three perpendicular four-fold axes of O now give D 4h subgroups, while the six two-fold axes give six D 2h subgroups. This group is isomorphic to S 4 × Z 2 (because both O and C i are normal subgroups), and is the symmetry group of the cube and octahedron. See also the isometries of the ...

  5. Symmetry - Wikipedia

    en.wikipedia.org/wiki/Symmetry

    The triskelion has 3-fold rotational symmetry. A geometric shape or object is symmetric if it can be divided into two or more identical pieces that are arranged in an organized fashion. [5] This means that an object is symmetric if there is a transformation that moves individual pieces of the object, but doesn't change the overall shape.

  6. Quintic threefold - Wikipedia

    en.wikipedia.org/wiki/Quintic_threefold

    One of the easiest examples to check of a Calabi-Yau manifold is given by the Fermat quintic threefold, which is defined by the vanishing locus of the polynomial = + + + + Computing the partial derivatives of gives the four polynomials = = = = = Since the only points where they vanish is given by the coordinate axes in , the vanishing locus is empty since [::::] is not a point in .

  7. Crystallographic restriction theorem - Wikipedia

    en.wikipedia.org/wiki/Crystallographic...

    The crystallographic restriction theorem in its basic form was based on the observation that the rotational symmetries of a crystal are usually limited to 2-fold, 3-fold, 4-fold, and 6-fold. However, quasicrystals can occur with other diffraction pattern symmetries, such as 5-fold; these were not discovered until 1982 by Dan Shechtman. [1]

  8. Category:3-folds - Wikipedia

    en.wikipedia.org/wiki/Category:3-folds

    In algebraic geometry, a 3-fold or threefold is a 3-dimensional algebraic variety. Pages in category "3-folds" The following 15 pages are in this category, out of 15 total.

  9. Screw axis - Wikipedia

    en.wikipedia.org/wiki/Screw_axis

    This multiple is indicated by a subscript. So, 6 3 is a rotation of 60° combined with a translation of one half of the lattice vector, implying that there is also 3-fold rotational symmetry about this axis. The possibilities are 2 1, 3 1, 4 1, 4 2, 6 1, 6 2, and 6 3, and the enantiomorphous 3 2, 4 3, 6 4, and 6 5. [8]

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