 | Acta Crystallographica Section A Acta Crystallographica Section A FOUNDATIONS AND ADVANCES |
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![[Figure 1]](dm5047fig1mag.jpg)
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Figure 1
(a) A family of tori which are coaxial with the spherical torus. This family fills up the volume of the three-dimensional sphere S3. The axis of the Boerdijk–Coxeter helix corresponds to the torus axis in the {3, 3, 5} polytope. (Adapted from Fig. 8 in Mosseri et al., 1985  .) (b) The Boerdijk–Coxeter helix obtained from regular tetrahedra. A simplicial seven-vertex complex of four tetrahedra with common vertex 1 is shown by black lines. Two such complexes are joined by a connected sum – the three tetrahedra between them (grey lines). (c) Representation of a cover over a bouquet of the circle S1 and the sphere S2 in the form of spheres attached to a screw line. On every sphere a solid common point with the screw line is shown, corresponding to a point of a manifold on S1. This point is the common vertex joining two seven-vertex complexes (Fig. 1b). (Adapted from Fig. 103b in Dubrovin et al., 2001.) (d) The projection of {4, 3, 3} polytope vertices on the catenoid (adapted from Fig. 9b in Mosseri et al., 1985), which is determined by the family of tori (Fig. 1a). (e) The transformation of catenoid (Fig. 1d) into helicoid via an intermediate surface (wound over the catenoid) – joining of catenoid and helicoid surfaces. Trajectories of the generatrix ends are marked by thick lines. (Adapted from Fig. 26 in Fomenko & Tuzhilin, 1992.) |
![[Figure 1]](dm5047fig1.jpg)
| FOUNDATIONS ADVANCES |
ISSN: 2053-2733
