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Morphological Analysis of Soil Aggregates Using Euler's Polyeder Formula
Author(s) -
Hartge Karl Heinrich,
Bachmann Joerg,
Pesci Nestor
Publication year - 1999
Publication title -
soil science society of america journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.836
H-Index - 168
eISSN - 1435-0661
pISSN - 0361-5995
DOI - 10.2136/sssaj1999.634930x
Subject(s) - polyhedron , subdivision , rounding , loess , mathematics , enhanced data rates for gsm evolution , geometry , combinatorics , computer science , geology , telecommunications , archaeology , geomorphology , history , operating system
In present morphologic analysis of soil aggregates, a subdivision between polyhedra and prisms is commonly performed using the relation between their axis lengths. Further description is limited to qualitative alternatives like “rounded/not rounded.” The objective of this study was to obtain a more detailed subdivision of polyhedra using a quantitative approach, thus satisfying a prerequisite for statistical analysis. A series of experiments were carried out to determine the shape of aggregates using the parameters of Euler's polyhedron formula, which states that the number of corners plus the number of faces is equal to the number of edges plus 2. Results were evaluated from sets of 10 aggregates from each of six sites and from several depths as well as from artificial new loess aggregates made from the material of one of the samples. The results indicate that the number of faces was the least variable term. Most aggregates were found to have five faces, so are called pentahedra. The number of edges is generally smaller on field aggregates than on perfect polyhedra. For artificial fresh loess aggregates, however, the number of edges corresponds more closely to that of perfect polyhedra. The number of corners is similar to those in perfect polyhedra in all cases. Thus the number of edges is the element that is most promising for a more detailed subdivision of soil aggregates. Even though there is a general correlation between number of faces and number of edges, the edge/face ratio can provide independent information on the degree of rounding. Difficulties in discerning faces, edges, and corners, and the individual influence of personal assessment by the observer have shown to be of minor importance.