Isoperimetric Quotient for Fullerenes and Other Polyhedral Cages

1997 ◽  
Vol 37 (6) ◽  
pp. 1028-1032 ◽  
Author(s):  
Tomaž Pisanski ◽  
Matjaž Kaufman ◽  
Drago Bokal ◽  
Edward C. Kirby ◽  
Ante Graovac
Keyword(s):  
Isoperimetric Quotient

scholarly journals Microstructure Measurement and Microgeometric Packing Characterization of Rigid Polyurethane Foam Defects

2017 ◽  
Vol 36 (4) ◽  
pp. 183-204 ◽  
Author(s):  
Jie Xu ◽  
Tao Wu ◽  
Jianwei Zhang ◽  
Hao Chen ◽  
Wei Sun ◽  
...  
Keyword(s):  
Relative Density ◽  
Cell Volume ◽  
Polyurethane Foams ◽  
Rigid Polyurethane Foam ◽  
Degree Of Anisotropy ◽  
Extensive Surface ◽  
Density Ratios ◽  
Geometric Relationship ◽  
Isoperimetric Quotient

Streak and blister cell defects pose extensive surface problems for rigid polyurethane foams. In this study, these morphological anomalies were visually inspected using 2D optical techniques, and the cell microstructural coefficients including degree of anisotropy cell circumdiameter, and the volumetric isoperimetric quotient were calculated from the observations. A geometric regular polyhedron approximation method was developed based on relative density equations, in order to characterize the packing structures of both normal and anomalous cells. The reversely calculated cell volume constant, Cc, from polyhedron geometric voxels was compared with the empirical polyhedron cell volume value, Ch. The geometric relationship between actual cells and approximated polyhedrons was characterized by the defined volumetric isoperimetric quotient. Binary packing structures were derived from deviation comparisons between the two cell volume constants, and the assumed partial relative density ratios of the two individual packing polyhedrons. The modelling results show that normal cells have a similar packing to the Weaire-Phelan model, while anomalous cells have a dodecahedron/icosidodecahedron binary packing.

scholarly journals On the Monotonicity of the Isoperimetric Quotient for Parallel Bodies

2021 ◽  
Vol 32 (1) ◽  
Author(s):  
Christian Richter ◽  
Eugenia Saorín Gómez
Keyword(s):  
Convex Body ◽  
Surface Area ◽  
Convex Bodies ◽  
The Family ◽  
Definition Of ◽  
Euclidean Setting ◽  
Isoperimetric Quotient ◽  
Arbitrary Gauge ◽  
Area And Volume

AbstractThe isoperimetric quotient of the whole family of inner and outer parallel bodies of a convex body is shown to be decreasing in the parameter of definition of parallel bodies, along with a characterization of those convex bodies for which that quotient happens to be constant on some interval within its domain. This is obtained relative to arbitrary gauge bodies, having the classical Euclidean setting as a particular case. Similar results are established for different families of Wulff shapes that are closely related to parallel bodies. These give rise to solutions of isoperimetric-type problems. Furthermore, new results on the monotonicity of quotients of other quermassintegrals different from surface area and volume, for the family of parallel bodies, are obtained.

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