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.