Truncated Rhombic Dodecahedron

The author H C Rajpoot has discovered a new polyhedron by truncating a rhombic dodecahedron from all its 24 edges so that newly generated 24 identical vertices exactly lie on a spherical surface. A truncated rhombic dodecahedron is a non uniform convex polyhedron having 12 congruent rectangular faces, 6 congruent square faces, 8 congruent equilateral triangular faces, 48 edges & 24 identical vertices.  The author, applying his theory of polygon, derives the formula to analytically compute the radius of circumscribed sphere passing through all 24 identical vertices, normal distances of rectangular, square & equilateral triangular faces from the centre of polyhedron, surface area, volume, solid angles subtended by rectangular, square & equilateral triangular faces at the centre of polyhedron by using ‘HCR’s Theory of Polygon’, dihedral angle between each two faces meeting at any of 24 identical vertices (i.e. truncated rhombic dodecahedron), solid angle subtended by truncated rhombic dodecahedron at any of its 24 identical vertices.

Published by Harish Chandra Rajpoot

He is studying for a PhD at Indian Institute of Technology Bombay. He received Master's degree (Hons) in Production Engineering from Indian Institute of Technology Delhi. He received Bachelor's degree (Hons) in Mechanical Engineering from M.M.M. Engineering College Gorakhpur (UP), India. He has passion for Mathematics specifically Geometry, Trigonometry, Algebra and Photometry in Mathematical Physics. He made independent researches in Mathematics over three years and proposed 'Theory of Polygon' for solid angle. He derived numerous formula & results and made remarkable contribution to Mathematics specifically Geometry. His areas of interest in Production Engineering are Laser Material Processing, Laser Machining, Smart Manufacturing, Modeling and Simulation in Manufacturing.

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