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I would like to know what the name is for the structure drawn below. This looks like a pyramid with 4 atoms at each vertex. Does the name of the structure depend on whether the atoms are all the same or if they are a combination of different ones?

enter image description here

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The current version of Nomenclature of Inorganic Chemistry – IUPAC Recommendations 2005 (Red Book) and the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) include polyhedra and corresponding polyhedral symbols that describe the geometrical configuration.

When an atom is attached to three atoms or groups (e.g. coordination compounds with a coordination number of three), the geometry may be trigonal planar or trigonal pyramidal. For the structure given in the question, the geometry is obviously trigonal pyramidal, not planar. Thus, the coordination polyhedron is a trigonal pyramid; the corresponding polyhedral symbol is TPY-3.

trigonal pyramid

This coordination polyhedron is not to be confused with a tetrahedron (polyhedral symbol: T-4), which applies to a coordination number of four, or an atom that is attached to four atoms or groups.

tetrahedron

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If the four faces of this shape are equilateral triangles, that would make this shape a tetrahedron (literally meaning four faces). This is the molecular shape associated with the $\mathrm{sp^3}$ hybridization. The shape is independent of what atoms constitute the corners.

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    $\begingroup$ Tetrahedra have central atoms. $\endgroup$
    – Mithoron
    Commented Jul 27, 2015 at 10:57
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    $\begingroup$ @Mithoron: no, they don't. $\endgroup$
    – Gerhard
    Commented Jul 27, 2015 at 16:00
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    $\begingroup$ Gerhard is right. As evidence, en.wikipedia.org/wiki/Tetrahedrane $\endgroup$
    – Curt F.
    Commented Jul 28, 2015 at 0:48
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    $\begingroup$ The argument about hybridisation of course only applies to (ideal) tetrahedra that have a central atom and to this central atom alone. $\endgroup$ Commented Jul 28, 2015 at 3:39
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    $\begingroup$ A tetrahedron is an abstract geometrical shape, just as a cube, a sphere or a dodecahedron. They only describe the shape of the body, not the content. They do not have anything to do with atoms, but are of course often used to describe the outer appearance of an arrangement of atoms in chemistry. $\endgroup$
    – Gerhard
    Commented Jul 28, 2015 at 8:41

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