Corrections to Crystallographic Groups of Four-Dimensional Space by Brown et al. (1978) [New York: Wiley and Sons]

There is an error in the tabulation of enantiomorphic space-group types given in the book Crystallographic Groups of Four-Dimensional Space by Brown et al. (1978). It has recently been found by one of us (BS) while extending the derivation of the enantiomorphism of crystallographic groups up to dimension 6. We refer to the terminology of the book.

In the book, it is wrongly claimed that the (affine) four-dimensional space-group type 08/01/01/002 splits into an enantiomorphic pair of (proper) space-group types. This is indicated in the book by an * preceding the space-group number on p. 118. This asterisk should be removed.

As a consequence of this error, the following changes have also to be made:

• 1. Page 11, last line of the section `Enantiomorphism': replace 112 by 111.

• 2. Page 52, in List 3.1A, Overall statistics: replace in the line `Number of space-group types' 4783 (112) by 4783 (111).

• 3. Page 53, in the line starting with VII: replace 24 (1) by 24 and 2 (1) by 2.

• 4. Page 407, line 2: delete the line `Family VII 08/01/01/002'.

In addition to the calculations by BS that led to the discovery of this error, J. N. and V. Felsch have also recalculated the classification of the four-dimensional crystallographic groups (including their enantiomorphism) using computer programs different from those used by BS. No further errors have been found. We cannot reconstruct how the error in the original listings occurred.

While reporting this error, we also want to point out another fact. In the theoretical introduction of the book, the definition of the term `crystal system', while working for dimensions up to four, was not dimension independent. A correction has been given by Neubüser et al. (1981).