4mm Point Group

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4mm Point Group

Table 3003 list all the space groups which have point group 4mm.

Table 3003. All space groups which have point group 4mm.

Space Group	Patterson Space Group	Number of Symmetry Operators	Crystal System	Laue Class	Lattice Type
P4mm	123	8	Tetragonal	4/mmm	P
P4bm	123	8	Tetragonal	4/mmm	P
P4₂cm	123	8	Tetragonal	4/mmm	P
P4₂nm	123	8	Tetragonal	4/mmm	P
P4cc	123	8	Tetragonal	4/mmm	P
P4nc	123	8	Tetragonal	4/mmm	P
P4₂mc	123	8	Tetragonal	4/mmm	P
P4₂bc	123	8	Tetragonal	4/mmm	P
I4mm	139	16	Tetragonal	4/mmm	I
I4cm	139	16	Tetragonal	4/mmm	I
I4₁md	139	16	Tetragonal	4/mmm	I
I4₁cd	139	16	Tetragonal	4/mmm	I

In 4mm, σ₁ and σ₃ are related by the 90° rotation of 4fold axis as shown in Figure 3003a. There are two obvious sets of mirror planes which are σ₁/σ₃ and σ₂/σ₄. These two sets are not equivalent as the operation of the rotation axis will never match the two sets to the same location. Therefore, this is group 4mm.

4mm point group

Figure 3003a. 4mm point group.

Practical Electron Microscopy and Database

An Online Book, Second Edition by Dr. Yougui Liao (2006)

4mm Point Group