Polyhedral symbols

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

  1. 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.
  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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