Mid-facets of a simplex

O184; The mid-facet of a simplex in n-dimensional Euclidean space which was introduced quite recently is an important geometric element.An analytic expression for the mid-facet area of a simplex is firstly given.In order to obtain the expression,the exterior differential method was presented.Further...

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Bibliographic Details
Published in:Applied mathematics and mechanics 2004-06, Vol.25 (6), p.679-685
Main Authors: Xiao-yan, Li, Bin-wu, He, Gang-song, Leng
Format: Article
Language:English
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Summary:O184; The mid-facet of a simplex in n-dimensional Euclidean space which was introduced quite recently is an important geometric element.An analytic expression for the mid-facet area of a simplex is firstly given.In order to obtain the expression,the exterior differential method was presented.Furthermore,the properties of the mid-facets of a simplex analogous to median lines of a triangle(such as for all mid-facets of a simplex,there exists another simplex such that its edge-lengths equal to these mid-facets area respectively,and all of the mid-facets of a simplex have a common point)were proved.Finally,by applying the analytic expression,a number of inequalities which combine edge-lengths,circumradius,median line,bisection area and facet area with the mid-facet area for a simplex were established.
ISSN:0253-4827
1573-2754
DOI:10.1007/BF02438211