TY - JOUR UR - http://lib.ugent.be/catalog/pug01:8509418 ID - pug01:8509418 LA - eng TI - Decoration of the truncated tetrahedron - an Archimedean polyhedron - to produce a new class of convex equilateral polyhedra with tetrahedral symmetry PY - 2016 JO - (2016) SYMMETRY-BASEL SN - 2073-8994 PB - 2016 AU - Schein, Stan AU - Yeh, Alexander J AU - Coolsaet, Kris WE02 001980172447 AU - Gayed, James M AB - The Goldberg construction of symmetric cages involves pasting a patch cut out of a regular tiling onto the faces of a Platonic host polyhedron, resulting in a cage with the same symmetry as the host. For example, cutting equilateral triangular patches from a 6.6.6 tiling of hexagons and pasting them onto the full triangular faces of an icosahedron produces icosahedral fullerene cages. Here we show that pasting cutouts from a 6.6.6 tiling onto the full hexagonal and triangular faces of an Archimedean host polyhedron, the truncated tetrahedron, produces two series of tetrahedral (T-d) fullerene cages. Cages in the first series have 28n(2) vertices (n >= 1). Cages in the second (leapfrog) series have 3 x 28n(2). We can transform all of the cages of the first series and the smallest cage of the second series into geometrically convex equilateral polyhedra. With tetrahedral (T-d) symmetry, these new polyhedra constitute a new class of "convex equilateral polyhedra with polyhedral symmetry". We also show that none of the other Archimedean polyhedra, six with octahedral symmetry and six with icosahedral, can host full-face cutouts from regular tilings to produce cages with the host's polyhedral symmetry. ER -Download RIS file
00000nam^a2200301^i^4500 | |||
001 | 8509418 | ||
005 | 20180816075855.0 | ||
008 | 170214s2016------------------------eng-- | ||
022 | a 2073-8994 | ||
024 | a 000382269100013 2 wos | ||
024 | a 1854/LU-8509418 2 handle | ||
024 | a 10.3390/sym8080082 2 doi | ||
040 | a UGent | ||
245 | a Decoration of the truncated tetrahedron - an Archimedean polyhedron - to produce a new class of convex equilateral polyhedra with tetrahedral symmetry | ||
260 | c 2016 | ||
520 | a The Goldberg construction of symmetric cages involves pasting a patch cut out of a regular tiling onto the faces of a Platonic host polyhedron, resulting in a cage with the same symmetry as the host. For example, cutting equilateral triangular patches from a 6.6.6 tiling of hexagons and pasting them onto the full triangular faces of an icosahedron produces icosahedral fullerene cages. Here we show that pasting cutouts from a 6.6.6 tiling onto the full hexagonal and triangular faces of an Archimedean host polyhedron, the truncated tetrahedron, produces two series of tetrahedral (T-d) fullerene cages. Cages in the first series have 28n(2) vertices (n >= 1). Cages in the second (leapfrog) series have 3 x 28n(2). We can transform all of the cages of the first series and the smallest cage of the second series into geometrically convex equilateral polyhedra. With tetrahedral (T-d) symmetry, these new polyhedra constitute a new class of "convex equilateral polyhedra with polyhedral symmetry". We also show that none of the other Archimedean polyhedra, six with octahedral symmetry and six with icosahedral, can host full-face cutouts from regular tilings to produce cages with the host's polyhedral symmetry. | ||
598 | a A1 | ||
100 | a Schein, Stan | ||
700 | a Yeh, Alexander J | ||
700 | a Coolsaet, Kris u WE02 0 001980172447 0 801000625810 | ||
700 | a Gayed, James M | ||
650 | a Mathematics and Statistics | ||
653 | a Goldberg polyhedra | ||
653 | a cages | ||
653 | a fullerenes | ||
653 | a tilings | ||
653 | a cutouts | ||
653 | a VIRUSES | ||
773 | t SYMMETRY-BASEL g Symmetry-Basel. 2016. 8 (8) q 8:8< | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/8509418/file/8547887 z [open] y symmetry-08-00082.pdf | ||
920 | a article | ||
852 | x WE b WE02 | ||
922 | a UGENT-WE |
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