This table contains the coordination geometries and polyhedral symbols for coordination numbers (CN) 1 to 20 as recommended in The Red Book [1] and expanded in the IUPAC Technical Report [2]. The polyhedral symbols proposed by Hartshorn et al. [2] are shown in light green background. Note that not all geometries listed as separate entries in the latter publication [2, Table 1] have polyhedral symbols assigned. The single neighbor (CN = 1) and linear (L-2) geometries do not correspond to any polygon or polyhedron. Coordination polygons TP-3 and SP-4 can be viewed as degenerate (zero-height) cases of pyramids TPY-3 and SPY-4, respectively.
CN | Coordination geometry | Alternative names | Polyhedral symbol |
---|---|---|---|
1 | single neighbor * | — | |
2 | angular ◊ | bent V-shaped |
A-2 |
2 | linear * | L-2 | |
3 | trigonal plane ◊ | triangular planar | TP-3 |
3 | trigonal pyramid | triangular non-coplanar | TPY-3 |
3 | T-shape ◊ | T-shaped | TS-3 |
4 | square plane ◊ | SP-4 | |
4 | square pyramid ▲ | square non-coplanar | SPY-4 |
4 | see-saw | SS-4 | |
4 | tetrahedron | triangular pyramid trigonal pyramid |
T-4 |
5 | pentagonal plane ◊ | pentagon | PP-5 |
5 | square pyramid ▲ | SPY-5 | |
5 | trigonal bipyramid | triangular dipyramid trigonal dipyramid |
TBPY-5 |
6 | octahedron | square bipyramid square dipyramid triangular antiprism trigonal antiprism |
OC-6 |
6 | pentagonal pyramid | PPY-6 | |
6 | trigonal prism | triangular prism | TPR-6 |
7 | octahedron, face monocapped | face-capped octahedron monocapped octahedron |
OCF-7 |
7 | pentagonal bipyramid | pentagonal dipyramid | PBPY-7 |
7 | trigonal prism, square face monocapped | augmented triangular prism | TPRS-7 |
7 | trigonal prism, end-trigonal face capped | augmented triangular prism | TPRT-7 † |
8 | cube | square prism tetragonal prism |
CU-8 |
8 | dodecahedron ‡ | dodecadeltahedron dodecahedron with triangular faces Siamese dodecahedron snub disphenoid triangular dodecahedron trigonal dodecahedron |
DD-8 |
8 | hexagonal bipyramid | hexagonal dipyramid | HBPY-8 |
8 | octahedron, trans-bicapped § | bicapped octahedron § | OCT-8 (3 isomers) § |
8 | square antiprism | anticube tetragonal antiprism |
SARP-8 |
8 | trigonal prism, square-face bicapped | TPRS-8 | |
8 | trigonal prism, triangular-face bicapped | TPRT-8 | |
9 | square-face capped square prism | monocapped cube | CUS-9 |
9 | heptagonal bipyramid | heptagonal dipyramid | HBPY-9 |
9 | square-face monocapped antiprism | gyroelongated square pyramid | SAPRS-9 (2 isomers) |
9 | triangular cupola | TCA-9 | |
9 | tricapped octahedron | TOCT-9 (2 isomers) | |
9 | trigonal prism, square-face tricapped ‖ | tricapped triangular prism ‖ triaugmented trigonal prism |
TPRS-9 (3 isomers) ‖ |
9 | tridiminished icosahedron | — | |
10 | bicapped square prism | bicapped cube | CUS-10 (2 isomers) |
10 | hexadecahedron | HDN-10 | |
10 | pentagonal antiprism | paradiminished icosahedron | PAPR-10 |
10 | pentagonal prism | PPR-10 | |
10 | square-face bicapped square antiprism | bicapped anticube gyroelongated square dipyramid |
SAPRS-10 |
10 | trigonal-face bicapped square antiprism | SAPRT-10 (3 isomers) | |
10 | metabidiminished icosahedron | — | |
10 | sphenocorona | — | |
11 | pentagonal-face capped pentagonal antiprism | gyroelongated pentagonal pyramid diminished icosahedron # truncated icosahedron ¶ |
PPRP-11 |
11 | hendecahedron | bisymmetric hendecahedron | — |
11 | sphenoid hendecahedron | — | |
11 | Cs-octahedron | — | |
11 | diminished icosahedron # | — | |
12 | hexagonal antiprism | HAPR-12 | |
12 | hexagonal prism | HPR-12 | |
12 | icosahedron | IC-12 | |
12 | pentagonal-face bicapped pentagonal prism | PPRP-12 | |
12 | anticuboctahedron | triangular bicupola triangular orthobicupola |
— |
12 | cuboctahedron | — | |
12 | sphenomegacorona | — | |
12 | square cupola | — | |
12 | truncated tetrahedron | — | |
20 | dodecahedron ⸸ | DD-20 |
* | Neither a polyhedron nor a polygon. |
◊ | A polygon. |
▲ | The Red Book gives the same name, ‘square pyramid’, to both SPY-4 and SPY-5 [1]. Hartshorn et al. use ‘square non-coplanar’ for SPY-4 [2, p. 1782]. |
† | Hartshorn et al. [2, Table 1, p. 1782] list TPRT-7 as if it were an IUPAC-recommended symbol, in spite of it not being mentioned in [1]. |
‡ | The Red Book names DD-8 ‘dodecahedron’ [1] which is unfortunate as this term is commonly understood to mean regular dodecahedron. Indeed, Hartshorn et al. propose to use ‘dodecahedron’ in this latter sense for DD-20. The name ‘dodecahedron with triangular faces’ for DD-8 [2, p. 1783] is more explicit but a bit long. My preference would be ‘dodecadeltahedron’. |
§ | The Red Book recommends OCT-8 for trans-bicapped octahedron [1] while Hartshorn et al. cite OCT-8 as a symbol for any of the three possible isomers of bicapped octahedron [2, p. 1783]. |
‖ | The Red Book recommends TPRS-9 for square-face tricapped trigonal prism [1] while Hartshorn et al. cite TPRS-9 as a symbol for any of the three possible isomers of tricapped triangular prism [2, p. 1783]. |
# | Hartshorn et al. list ‘diminished icosahedron’ as one of the synonyms for PPRP-11 and later as a separate term without any corrresponding polyhedral symbol [2, p. 1783]. As far as I know diminished icosahedron and pentagonal-face capped pentagonal antiprism are exactly the same. |
¶ | Hartshorn et al. list ‘truncated icosahedron’ as one of the synonyms for PPRP-11 [2, p. 1783]. However, this name normally refers to an Archimedean solid that has 60 vertices. A well-known example of truncated icosahedron in chemistry is buckminsterfullerene C60 (buckyball). I doubt there is such thing as a 60-coordinate complex. |
⸸ | Now this is the dodecahedron. |
References
- Connelly, N.G., Hartshorn R.M., Damhus, T. and Hutton, A.T. Nomenclature of Inorganic Chemistry: IUPAC Recommendations 2005. Royal Society of Chemistry, Cambridge, 2005, p. 176, Table IR-9.2.
- Hartshorn, R.M., Hey-Hawkins, E., Kalio, R. and Leigh, G.J. (2007) Representation of configuration in coordination polyhedra and the extension of current methodology to coordination numbers greater than six (IUPAC Technical Report). Pure and Applied Chemistry 79, 1779—1799.
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