# THE POLYTOPES WITH REGULAR-PRISMATIC VERTEX FIGURES by Coxeter

By Coxeter

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81. For read , 360, line 21. Interchange 2 and r [or any other pair). 360, line 23. Interchange 1 and T"1 (or any other pair). 361, line 15. For ± 3 read 3. 369, line 9. For an nth read a tn. 388, line 21. Insert — after — 1, . semicolon. Ignore the comma before the second 406, line 23. For [1357 . 2468] T = T1357 ST2468 read ST [1357. 2468] = ST1357ST2468. 408, line 15. For automorphism read automorphisms. 2. Miller's proof that every finite uniform polytope has a drcumcentre*. A set of points are said to be equivalent if, for every pair A, B of the points, there exists a congruent transformation which changes A into B, leaving the set unchanged as a whole.

Annalen, 14 (1878), 111-172. , 1-5 (1882-4). , "Ueber den Begriff des functionen Lheoretischen Fundamentalbereichs", Math. Avnalcn, 40 (1891), 130-139. , " Zur Theorie der automorphen Funktionen von beliebig vielen Variabeln ", Math. Annalen, 61 (1905), 325-368. , "Ueber die Bewegungsgruppen der Euklidischen Raume", 1 Abhandlung, Math. Annalen, 70 (1910), 297-336 ; 2 Abhandlung, Math. Annalen, 72 (1911), 400-412. Forsyth, A. , Theory of functions of a complex variable, 3rd ed. (1918;, 653-793. ] POLYTOPES WITH REGULAR-PRISMATIC VERTEX FIGURES 189 INDEX.

Taking the latter value, we have Q = [145 . 126](13). 126] = # 4 . Moreover, (13) = (61)(36)(61). 5, and Q= HQH2H0HiH0H2HQ. 11) we obtain an abstract definition for the group in terms of the /J's, and so ultimately in terms of the two operations cu and Ho. But the new abstract definition is excessively complicated; in fact, the definition in terms of six operations is altogether preferable. 5. 5) the group of automorphisms of the bitangents of a plane quartic of genus 3. By (16 . 75) it has the abstract definition Q'3=l, (P/ Qy = (Q'N^f = (Q' (P' Q'-i)2 = For simplicity we have written N' for 'N')* = (N'P1)* = 1.