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  2. Torus - Wikipedia

    en.wikipedia.org/wiki/Torus

    Poloidal direction (red arrow) and toroidal direction (blue arrow) A torus can be parametrized as: [2] (,) = (+ ⁡) ⁡ (,) = (+ ⁡) ⁡ (,) = ⁡. using angular coordinates , [,), representing rotation around the tube and rotation around the torus' axis of revolution, respectively, where the major radius is the distance from the center of the tube to the center of the torus and the minor ...

  3. Double bond - Wikipedia

    en.wikipedia.org/wiki/Double_bond

    In chemistry, a double bond is a covalent bond between two atoms involving four bonding electrons as opposed to two in a single bond. Double bonds occur most commonly between two carbon atoms, for example in alkenes. Many double bonds exist between two different elements: for example, in a carbonyl group between a carbon atom and an oxygen atom.

  4. Compound of two tetrahedra - Wikipedia

    en.wikipedia.org/wiki/Compound_of_two_tetrahedra

    A facetting of a rectangular cuboid, creating compounds of two tetragonal or two rhombic disphenoids, with a bipyramid or rhombic fusil cores. This is first in a set of uniform compound of two antiprisms. A facetting of a trigonal trapezohedron creates a compound of two right triangular pyramids with a triangular antiprism core.

  5. Manifold - Wikipedia

    en.wikipedia.org/wiki/Manifold

    After a line, a circle is the simplest example of a topological manifold. Topology ignores bending, so a small piece of a circle is treated the same as a small piece of a line. Considering, for instance, the top part of the unit circle, x 2 + y 2 = 1, where the y-coordinate is positive (indicated by the yellow arc in Figure 1).

  6. Isomer - Wikipedia

    en.wikipedia.org/wiki/Isomer

    A double bond between two carbon atoms forces the remaining four bonds (if they are single) to lie on the same plane, perpendicular to the plane of the bond as defined by its π orbital. If the two bonds on each carbon connect to different atoms, two distinct conformations are possible, that differ from each other by a twist of 180 degrees of ...

  7. Amplituhedron - Wikipedia

    en.wikipedia.org/wiki/Amplituhedron

    Amplituhedron. Notional amplituhedron visualization. In mathematics and theoretical physics (especially twistor string theory), an amplituhedron is a geometric structure introduced in 2013 by Nima Arkani-Hamed and Jaroslav Trnka. It enables simplified calculation of particle interactions in some quantum field theories.

  8. Tetrahedron - Wikipedia

    en.wikipedia.org/wiki/Tetrahedron

    Not to be confused with tetrahedroid, Tetraedron, or Tetrahedron (journal). In geometry, a tetrahedron (pl.: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertices. The tetrahedron is the simplest of all the ordinary convex polyhedra.

  9. Orbital hybridisation - Wikipedia

    en.wikipedia.org/wiki/Orbital_hybridisation

    In chemistry, orbital hybridisation (or hybridization) is the concept of mixing atomic orbitals to form new hybrid orbitals (with different energies, shapes, etc., than the component atomic orbitals) suitable for the pairing of electrons to form chemical bonds in valence bond theory. For example, in a carbon atom which forms four single bonds ...

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