Table for uniform trapezohedrons with congruent right kite faces

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Table of the generalized formula applicable on any uniform polyhedron having 2n congruent right kite faces, 4n edges & 2n+2 vertices lying on a spherical surface with a certain radius. These formula have been derived by the author Mr H.C. Rajpoot to analyse infinite no. of the uniform polyhedrons having congruent right kite faces simply by setting n=3,4,5,6,7,………………upto infinity, to calculate all the important parameters such as ratio of unequal edges, outer radius, inner radius, mean radius, surface area, volume, solid angles subtended by the polyhedron at its vertices, dihedral angles between the adjacent right kite faces etc. These formula are very useful for the analysis, modeling & designing of various uniform polyhedrons.

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Mathematical analysis of uniform polyhedron trapezohedron with congruent right kite faces: Let there be any uniform polyhedron trapezohedron having vertices edges congruent faces each as a right kite with two pairs of unequal sides edges of then all its important parameters are determined as tabulated below Inner inscribed radius Outer circumscribed radius √ Mean radius √ Surface area √ Volume √ A uniform polyhedron trapezohedron has two unequal sides edges in a ratio given as √ Each right kite face of uniform polyhedron has one acute angle given as follows √ two right angles one obtuse angle Estimated illustrated by Mr Harish Chandra Rajpoot B Tech Mechanical Engineering M.M.M. University of Technology Gorakhpur-273010 UP India April 2015

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