Birss Symmetry & Magnetism — Transcription Project

Markdown transcriptions of selected tables from:

R. R. Birss, Symmetry and Magnetism, North-Holland / Elsevier, 1966. Free online access: Internet Archive

This project digitises the key reference tables into clean, cross-referenced Markdown, and compares them with the corresponding tables in the International Tables for Crystallography (ITC).

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Files

File	Contents
conventions-reference.md	Master reference: coordinate conventions, notation systems (HM / Schoenflies / Shubnikov), the σ(0)–σ(9) generating matrix pool, tensor type definitions (polar/axial, i-/c-tensor), and the complete cross-reference guide for all tables. Read this first.
birss-tables.tex	LaTeX source compiling the transcribed tables into a single typeset document.
birss-tables.pdf	Compiled PDF of the tables.
table-3.md	The 32 crystallographic point groups — symmetry operations, Schoenflies / HM / Shubnikov symbols, and generating matrices.
table-4a.md	Symbol-equivalence mapping: assigns each of the 32 point groups a letter symbol class (A–U) for each tensor type (polar/axial × even/odd rank). Gateway to Tables 4b–4f.
table-4b.md	Tensor forms, rank 0 (scalars) across all 32 point groups.
table-4c.md	Tensor forms, rank 1 (vectors) across all 32 point groups.
table-4d.md	Tensor forms, rank 2 across all 32 point groups.
table-4e.md	Tensor forms, rank 3 across all 32 point groups.
table-4f.md	Tensor forms, rank 4 across all 32 point groups.
table-6.md	The 90 magnetic point groups (32 classical + 58 black-and-white), with generating matrices including primed (time-reversal-combined) operations.
table-7.md	Magnetic point groups mapped to i-tensor and c-tensor symbol classes (extensions of the Table 4a scheme to magnetically ordered materials).
birss-itc-comparison.md	Comparison of Birss's tables with the corresponding International Tables for Crystallography (ITC) entries.

How to use

1. Start with conventions-reference.md to understand the notation.
2. Look up a point group in table-3.md to find its symbol and generating matrices.
3. Use table-4a.md to find the symbol class for the tensor type and rank you need.
4. Look up that symbol class in the appropriate table-4b through table-4f.

For magnetic point groups, follow the same chain starting from table-6.md and table-7.md.

Note on the 32 "grey" groups: The 32 Type II (grey) magnetic point groups are omitted from Tables 6 and 7 because their i-tensors are identical to the classical groups in Table 3, and their c-tensors are identically zero.