All the important parameters of a truncated icosidodecahedron

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Table of all the important parameters of a truncated icosidodecahedron (having 20 congruent equilateral triangular faces, 30 congruent golden rectangular faces & 12 congruent regular pentagonal faces) 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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Analysis of Truncated Icosidodecahedron with golden rectangles: Let there be any truncated icosidodecahedron having 20 congruent equilateral triangular faces each of edge length 30 congruent golden rectangular faces each of size 12 congruent regular pentagonal faces each of edge length 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 icosidodecahedron Solid angle subtended by each face at the centre of given truncated icosidodecahedron in Ste-radian sr Equilateral triangle 20 √ √ √ √ √ Golden rectangle 30 √ √ √ √ Regular pentagon 12 √ √ √ √ √ Inner inscribed radius √ √ √ Outer circumscribed radius √ √ Mean radius √ Surface area √ √ √ Volume √ When a solid truncated icosidodecahedron having golden rectangles 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 faces each with edge length 30 congruent rectangular faces each of size 12 congruent regular pentagonal faces each with edge length . This solid has two unequal edges in a ratio of which is also generated by truncating all 30 identical vertices of an icosidodecahedron 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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