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Geometry |
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Authors: Harish Chandra Rajpoot
In this paper, the generalized formula has been derived that is applicable to locate any sphere, with a certain radius, resting in a vertex (corner) at which n no. of edges meet together at angle α between any two consecutive of them such as the vertex of platonic solids, any of two identical & diagonally opposite vertices of trapezohedron (uniform polyhedron with congruent right kite faces) & the vertex of right pyramid with regular n-gonal base. These are also useful for filleting the faces meeting at the vertex of the polyhedron to best fit the sphere in that vertex. These are used to determine the distance of the sphere from the vertex, the distance of the sphere from the edges, the fillet radius of the faces, etc. The formula has been generalized for packing the spheres in the vertices of right pyramids & all five platonic solids.
Comments: 28 Pages, 6 Figures
Download: PDF
[v1] 2026-02-06 00:26:58
Unique-IP document downloads: 83 times
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