All the important parameters of a truncated dodecahedron

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Table of all the important parameters of a truncated dodecahedron (having 20 congruent equilateral triangular & 12 congruent regular decagonal faces each of equal edge length) such as normal distances & solid angles subtended by the faces, inner radius, outer radius, mean radius, surface area & volume calculated by using HCR's formula for regular polyhedrons. It can be used in analysis, designing & modelling of polyhedrons.

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HCR’s Formula for Regular n-Polyhedrons Analysis of Truncated Dodecahedron: Let there be any truncated dodecahedron having 20 congruent equilateral triangular 12 congruent regular decagonal faces each of edge length a then all its important parameters are calculated as tabulated below Congruent polygonal faces No. of faces Normal distance of each face from the centre of the given truncated dodecahedron Solid angle subtended by each face at the centre of the given truncated dodecahedron in Ste-radian sr Equilateral triangle 20 √ √ √ √ √ Regular decagon 12 √ √ √ √ √ Inner inscribed radius √ √ √ Outer circumscribed radius √ √ Mean radius √ Surface area √ Volume √ When a solid truncated dodecahedron of the maximum volume is produced from a solid sphere having certain diameter then approximate of total volume of the parent sphere is removed as scraps in facing operations to generate 20 congruent equilateral triangular 12 congruent regular decagonal faces each of equal edge length. Estimated illustrated by Mr Harish Chandra Rajpoot B Tech Mechanical Engineering M.M.M. University of Technology Gorakhpur-273010 UP India Dec 2014

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