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Geometry |
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Authors: Harish Chandra Rajpoot
In the present work, general analytical expressions are derived for the fundamental geometric properties of a disphenoid using three-dimensional coordinate geometry. Specifically, closed-form formulae are obtained for the volume and total surface area, as well as for the radii of the inscribed and circumscribed spheres, and solid angle subtended by disphenoid at its vertex. In addition, explicit coordinates of the four vertices are determined, together with the coordinates of the in-center, circum-center, and centroid of the disphenoid. The proof for in-center, circum-center and centroid to be coincident is presented and mathematical equation governing all disphenoids is also derived in a closed form.
Comments: 12 Pages. 4 Figures
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[v1] 2026-02-06 19:53:44
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