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Frequencies of n ‐polygons in planar sections of polyhedrons
Author(s) -
Voss Klaus
Publication year - 1982
Publication title -
journal of microscopy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.569
H-Index - 111
eISSN - 1365-2818
pISSN - 0022-2720
DOI - 10.1111/j.1365-2818.1982.tb00443.x
Subject(s) - polyhedron , planar , simple (philosophy) , geometry , mathematics , combinatorics , computer science , computer graphics (images) , philosophy , epistemology
SUMMARY In geology and metallography thin or polished sections of crystalline aggregates are a main subject of microscopic investigations. It is important to know what kinds of polygons are generated by planar sections through polyhedrons. In recent years computer simulation was the common method to determine the frequencies of n ‐polygons. In this paper an integral geometric approach to derive exact formulas for these frequencies is described. For some families of simple polyhedrons results are given in analytical form and as numerical values.