Is the completeness of the 230 known space groups in three dimensions proven?

Question

Wikipedia's Space group; History includes the passage below. While it mentions a proof for the 17 wallpaper groups in two dimensions, the word "proof" doesn't occur again in the article.

Is it settled now that there are exactly 230 possible space groups in three dimensions; that the current list is correct and complete?

If so, is it possible to cite a formal proof of this?

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Space groups in 2 dimensions are the 17 wallpaper groups which have been known for several centuries, though the proof that the list was complete was only given in 1891, after the much more difficult classification of space groups had largely been completed. In 1879 the German mathematician Leonhard Sohncke listed the 65 space groups (called Sohncke groups) whose elements preserve the chirality. More accurately, he listed 66 groups, but both the Russian mathematician and crystallographer Evgraf Fedorov and the German mathematician Arthur Moritz Schoenflies noticed that two of them were really the same. The space groups in three dimensions were first enumerated in 1891 by Fedorov (whose list had two omissions (I43d and Fdd2) and one duplication (Fmm2)), and shortly afterwards in 1891 were independently enumerated by Schönflies (whose list had four omissions (I43d, Pc, Cc, ?) and one duplication (P421m)). The correct list of 230 space groups was found by 1892 during correspondence between Fedorov and Schönflies. Barlow (1894) later enumerated the groups with a different method, but omitted four groups (Fdd2, I42d, P421d, and P421c) even though he already had the correct list of 230 groups from Fedorov and Schönflies; the common claim that Barlow was unaware of their work is incorrect. Burckhardt (1967) describes the history of the discovery of the space groups in detail.

Answer 1

A new algebraic solution has also been given, based on the Zassenhaus algorithm to determine the conjugacy classes of finite subgroups of $GL_3(\Bbb Z)$. The result is again $219$, respectively $230$ if we distinguish between mirror images. So there can't be "more".

References: An Algebraic Classification of the Three-Dimensional Crystallographic Groups

Counting crystallographic groups in low dimensions

Answer 2

Yes, it is possible, Conway et al. did it in a new way in the Beitraege. See the references in the Wikipedia article.

A pdf can be found here.