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 | 20181113145058.0 | ||
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 9 F4390D76-F0ED-11E1-A9DE-61C894A0A6B4 | ||
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 | ||
Z30 | x WE 1 WE02 | ||
922 | a UGENT-WE |
All data below are available with an Open Data Commons Open Database License. You are free to copy, distribute and use the database; to produce works from the database; to modify, transform and build upon the database. As long as you attribute the data sets to the source, publish your adapted database with ODbL license, and keep the dataset open (don't use technical measures such as DRM to restrict access to the database).
The datasets are also available as weekly exports.