Categorisation by Class: Non-Crystallographic

• Symmetry Home

• Crystal classes
• Unit cells
• Piezo/Pyroelectric classes

• Operations
• Dipole transitions
• Direct products
• Correlation tables
• Isomorphism
• Periodicity

• Stereographs
• 3D objects
• Molecules (non-java)
• Molecules (interactive)

• Links
• Live 3D
• References

• E-mail me

   

• Jon Goss
• AIMPRO

Cubic			(T Th O Td Oh)
Tetragonal			(C4 S4 C4h D4 C4v D2d D4h)
Orthorhombic			(D2 C2v D2h)
Monoclinic			(C2 Cs C2h)
Triclinic			(C1 Ci)
Trigonal			(C3 S6 D3 C3v D3d)
Hexagonal			(C6 C3h C6h D6 C6v D3h D6h)
Non-crystallographic*
Operations	Order	Schönflies Symbol	International Symbol	Full Symmetry Symbol	Correlation Table	Irred. Rep. products	× i	Isomorph. with
E, 2C∞φ	∞	C∞	∞	-		-	C∞h
E, 2C∞φ, i, 2S∞φ	∞	C∞h	∞/m	-		-	C∞h
E, 2C∞φ,∞σv	∞	C∞v	∞m	-		-	D∞h
E, 2C∞φ,∞σv, i, 2S∞φ,∞C2	∞	D∞h	∞/mm	-		-	D∞h
E, C5, C52, C53,  C54	5	C5	5	-		⊗	S10
E, S8, C4, S83, C2, S85, C43, S87	8	S8	-	-		⊗	C8h
E, 2C5, 2C52, 5C2	10	D5	-	-		⊗	D5d	C5v
E, 2C5, 2C52, 5σv	10	C5v	-	-		⊗	D5d	D5
E, C5, C52, C53, C54, σh, S5, S57, S53, S59	10	C5h	-	-		⊗	C10h
E, 2S8, 2C4, 2S83, C2, 4C2’, 4σd	16	D4d	-	-		⊗	D8h
E, 2C5, 2C52, 5C2, i, 2S10, 2S103, 5σd	20	D5d	-	-		⊗	D5d	D5h
E, 2C5, 2C52, 5C2, σh, 2S5, 2S52, 5σd	20	D5h	-	-		⊗	D10h	D5d
E, 2S12, 2C6, 2S4, 2C3, 2S125, C2, 6C2’, 6σd	24	D6d	-	-		⊗	D12h
E, 12C5, 12C52, 20C3, 15C2	60	I	-	-		⊗	Ih
E, 12C5, 12C52, 20C3, 15C2, i, 12S10, 12S103, 20S6, 15σ	120	Ih	-	-		⊗	Ih
All

This table lists point group symmetries along with their symmetry operations, the order of the group (i.e. the number of symmetry operations) and common notations.links to a correlation table, and ⊗ links to tables of products of irreducible representations. The group produced by combination with inversion is listed under "× i". This, in the case of crystolographic point groups, is the Laue class which corresponds to the symmetry of reciprocal space. Isomorphic groups are also listed where character tables are available.