The Mathematical Intelligencer. Volume 25. Issue 2

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6) Lay a carpet of S's on each e(n)-face and a carpet of F's on each f(n)-face, adding fringes of F's. 7. The side view (Fig. 8) shows that the outer shell of the complete model is cheiral, unlike the Type A shell (Fig. 13. 12). The proof that Types A and B are the only ones possi­ ble follows from a generalisation of Figure 12. We simply have to replace the segment dK by the diameter of a K(n), which is n times as long. The segments dF and ds remain unchanged. Thus the whole K(n + 1) is covered by a layer of rhombohedra no more than four deep.

3) Lay a carpet of F's, cheirally, on each of the c(n)-faces, and add fringes of S's. (4) Lay a second carpet of F 's on each of the first, and add a carpet of S 's to each d(n)-face. (5) Tum the model over and add a second carpet of S's to each carpet on a d(n)-face. (6) Lay a carpet of S's on each e(n)-face and a carpet of F's on each f(n)-face, adding fringes of F's. 7. The side view (Fig. 8) shows that the outer shell of the complete model is cheiral, unlike the Type A shell (Fig. 13. 12).

Longuet-Higgins, M . S . , Learning and Exploring with RHOMBO. Del Mar, USA, Dextra Mathematical Toys, 1 992. 1 1 . , O ber die Rhombenisoeder. Glasnik maternaticko-fizicki i astronorneski, 1 5 (1 960), 251 -262. 1 2. Unkelbach, H . , Die kantensymmetrisch gleichkantigen Polyeder. Deutsche Mathematik 5 Springer (1 940), 306-31 6. j Dav i d E . From KOnigsberg to GOttingen: A Sketch of H i l bert's Early Career David E. Rowe Send submissions to David E. Rowe, Rowe , E d itor D I avid Hilbert's remarkable career falls into two clearly distinct peri­ ods: the quiet Konigsberg phase, from his birth on 23 January 1862 to his full maturity as one of Germany's leading mathematicians, followed by the tu­ multuous Gottingen years.