Browsing by Type "conference proceeding"

Mathematical beading can be utilized for the construction of aesthetically pleasing sculptures inspired by a rich variety of shapes and forms in the nanoworld. Depending on the shapes of beads utilized, the resulting bead sculptures can be classified into two broad categories: (1) hard-sphere open packing models based on spherical beads, which include finite fullerenes, carbon nanotubes, carbon nanotori, curved three-dimensional graphitic surfaces, and space- filling tetrahedral zeolite structures and many inorganic coordination complexes such as extended metal atom chains; (2) truss-like frameworks constructed from tubular bugle beads, which can mimic the polyhedral representations of microscopic inorganic structures and many macroscopic space frames. Moverover, the hard-sphere open packing model for any polyhedral hydrocarbon of general formula C2nH2n can be achieved by cross-linkings of n pre- made five-bead chains without using any beading process. The assembly processes of certain symmetric polyhedral molecules, such as three Platonic hydrocarbons including tetrahedrane, cubane, and dodecahedrane, are similar to solving interlocking puzzles. Hence, these bead-chain models can also be regarded as a new type of take-apart put-together puzzle.

We introduce a new type of construction set which can be used to build valence sphere models of any cage-like hydrocarbon, of general formula (CH)2n. Using n linear five-bead chains, one can connect these building units into a three-dimension arrangement that stands for its valence sphere model through n cross-linkings. More interestingly, the assembly processes of certain symmetric molecules, such as three Platonic hydrocarbons, including tetrahedrane, cubane, and dodecahedrane, are similar to solving interlocking puzzles. Hence, a bead chain construction set can also be considered as a new type of take-apart put-together puzzles.

共同作者：倪茂庭、劉華美