Lecture 12 • Autumn 2026

Space Groups & the
International Tables for Crystallography

Learn to read an ITC space-group page: how a point group is added to a lattice to build an object diagram, how a symmetry diagram is derived from it, and how the full Hermann–Mauguin symbol is assembled.

Learning to Read the Tables

Anatomy of an ITC Space-Group Page

Every entry in Volume A follows the same layout. Click the hotspots to learn what each block means (Ref: ITC Vol. A).

C2/c No. 15
2/m Monoclinic
1
2
Object Diagram (General Position)
3
Origin at \(\bar{1}\) on glide plane c
Asymmetric unit: \( 0 \le x \le 1/2; \quad 0 \le y \le 1/2; \quad 0 \le z \le 1/2 \)
4
Symmetry operations
For (0,0,0) + set
(1) 1
(2) 2 \(0,y,1/4\)
(3) \(\bar{1}\) \(0,0,0\)
(4) c \(x,0,z\)
For (1/2,1/2,0) + set
(1) \(t(1/2,1/2,0)\)
(2) \(2_1\) \((0,1/2,0)\) \(1/4,y,1/4\)
(3) \(\bar{1}\) \(1/4,1/4,0\)
(4) n \((1/2,0,1/2)\) \(x,1/4,z\)
5
Positions
Mult. Wyckoff Site Sym. Coordinates
8f1 (1) x, y, z     (2) -x, y, -z+1/2
(3) -x, -y, -z   (4) x, -y, z-1/2
4e2 0, y, 1/4
6
Interactive Space-Group Engines

Explore Specific Space Groups

Select a space group below to launch its dedicated 3D interactive construction engine.

\( P1 \)

ITC No. 1 · Triclinic

\( P\bar{1} \)

ITC No. 2 · Triclinic

\( P2 \)

ITC No. 3 · Monoclinic

\( P2_1 \)

ITC No. 4 · Monoclinic

\( C2 \)

ITC No. 5 · Monoclinic

\( Pm \)

ITC No. 6 · Monoclinic

\( P2/c \)

ITC No. 13 · Monoclinic

\( C2/c \)

ITC No. 15 · Monoclinic
Graphical Language of ITC

Symmetry Symbol Flashcards

Practice Assessment

Did It Sink In? - 12

Test your mastery of screw axes, graphical symbols for mirrors and glides, the monoclinic space groups, and how an ITC space-group page is built: object diagrams, origin choice, asymmetric units and special positions.

Take the Quiz