LI Xiao-yan, HE Bin-wu, LENG Gang-song. Mid-Facets of a Simplex[J]. Applied Mathematics and Mechanics, 2004, 25(6): 621-626.
Citation: LI Xiao-yan, HE Bin-wu, LENG Gang-song. Mid-Facets of a Simplex[J]. Applied Mathematics and Mechanics, 2004, 25(6): 621-626.

Mid-Facets of a Simplex

  • Received Date: 2002-09-01
  • Rev Recd Date: 2003-11-25
  • Publish Date: 2004-06-15
  • 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.
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