 |
 |
Geometry |
|
Authors: Harish Chandra Rajpoot
In this paper, the circumscribed radius of a rhombicuboctahedron is derived using an alternative geometrical approach based on HCR’s Theory of Polygon. An explicit analytical expression is obtained for the radius of the circumscribed sphere passing through all 24 congruent vertices of a rhombicuboctahedron with a given edge length. Using the same theoretical framework, closed-form formulae are subsequently derived for the normal distances of the equilateral triangular and square faces from the centre, the total surface area, and the enclosed volume. In addition, analytical expressions are presented for the solid angles subtended at the centre by each equilateral triangular face and each square face, the dihedral angles between any two faces meeting at a vertex, and the solid angle subtended by the rhombicuboctahedron at any of its 24 identical vertices.
Comments: 18 Pages, 11 Figures
Download: PDF
[v1] 2026-02-05 23:17:43
Unique-IP document downloads: 86 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.
| Third-Party Links: |
|