TY  - JOUR
A1  - Hyde, Stephen T.
A1  - Evans, Myfanwy E.
T1  - Symmetric tangled Platonic polyhedra
JF  - Proceedings of the National Academy of Sciences of the United States of America
N2  - Conventional embeddings of the edge-graphs of Platonic polyhedra, {f,z}, where f,z denote the number of edges in each face and the edge-valence at each vertex, respectively, are untangled in that they can be placed on a sphere (S-2) such that distinct edges do not intersect, analogous to unknotted loops, which allow crossing-free drawings of S-1 on the sphere. The most symmetric (flag-transitive) realizations of those polyhedral graphs are those of the classical Platonic polyhedra, whose symmetries are *2fz, according to Conway's two-dimensional (2D) orbifold notation (equivalent to Schonflies symbols I-h, O-h, and T-d). Tangled Platonic {f,z} polyhedra-which cannot lie on the sphere without edge-crossings-are constructed as windings of helices with three, five, seven,... strands on multigenus surfaces formed by tubifying the edges of conventional Platonic polyhedra, have (chiral) symmetries 2fz (I, O, and T), whose vertices, edges, and faces are symmetrically identical, realized with two flags. The analysis extends to the "theta(z)" polyhedra, {2,z}. The vertices of these symmetric tangled polyhedra overlap with those of the Platonic polyhedra; however, their helicity requires curvilinear (or kinked) edges in all but one case. We show that these 2fz polyhedral tangles are maximally symmetric; more symmetric embeddings are necessarily untangled. On one hand, their topologies are very constrained: They are either self-entangled graphs (analogous to knots) or mutually catenated entangled compound polyhedra (analogous to links). On the other hand, an endless variety of entanglements can be realized for each topology. Simpler examples resemble patterns observed in synthetic organometallic materials and clathrin coats in vivo.
KW  - regular polyhedra
KW  - compound polyhedra
KW  - helicates
KW  - metal-organic
KW  - frameworks
KW  - clathrin
Y1  - 2022
U6  - https://doi.org/10.1073/pnas.2110345118
SN  - 0027-8424
SN  - 1091-6490
VL  - 119
IS  - 1
PB  - National Acad. of Sciences
CY  - Washington
ER  - 
TY  - JOUR
A1  - Wessig, Pablo
A1  - Gerngroß, Maik
A1  - Pape, Simon
A1  - Bruhns, Philipp
A1  - Weber, Jens
T1  - Novel porous materials based on oligospiroketals (OSK)
JF  - RSC Advances : an international journal to further the chemical sciences
N2  - New porous materials based on covalently connected monomers are presented. The key step of the synthesis is an acetalisation reaction. In previous years we used acetalisation reactions extensively to build up various molecular rods. Based on this approach, investigations towards porous polymeric materials were conducted by us. Here we wish to present the results of these studies in the synthesis of 1D polyacetals and porous 3D polyacetals. By scrambling experiments with 1D acetals we could prove that exchange reactions occur between different building blocks (evidenced by MALDI-TOF mass spectrometry). Based on these results we synthesized porous 3D polyacetals under the same mild conditions.
KW  - microporous organic polymers
KW  - molecular rods
KW  - construction
KW  - frameworks
KW  - membranes
KW  - sorption
KW  - models
Y1  - 2014
U6  - https://doi.org/10.1039/c4ra04437a
SN  - 2046-2069
VL  - 2014
IS  - 4
SP  - 31123
EP  - 31129
ER  -