Table of the important parameters for locating sphere in the vertex
Table of the generalized formula derived here by the author are 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 uniform polyhedrons with congruent right kite faces & the vertex of right pyramid with regular ngonal base. These are used to determine the distance of sphere from the vertex, distance of the sphere from the edges, fillet radius of the faces etc. These formula are also useful for packing the spheres in the vertices of platonic solids.
Tags:
Corner , Important , Locating , Parameters , Polyhedron
By:
harishchandraraj
Education
57 months ago
Download

Mathematical analysis of sphere resting in the vertex of polyhedrons
The generalized formula derived here by the author are 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 uniform polyhedrons with congruent right kite faces & the vertex of right pyramid with regular ngonal 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 sphere from the vertex, distance of sphere from the edges, fillet radius of the faces etc. The formula have been generalized for packing the spheres in the vertices of right pyramids & all five platonic solids.
Tags:
Analysis , Corner , Mathematical , Polyhedrons , REGULAR
By:
harishchandraraj
Education
57 months ago
Download

Table for uniform trapezohedrons with congruent right kite faces
Table of the generalized formula applicable on any uniform polyhedron having 2n congruent right kite faces, 4n edges & 2n+2 vertices lying on a spherical surface with a certain radius. These formula have been derived by the author Mr H.C. Rajpoot to analyse infinite no. of the uniform polyhedrons having congruent right kite faces simply by setting n=3,4,5,6,7,………………upto infinity, to calculate all the important parameters such as ratio of unequal edges, outer radius, inner radius, mean radius, surface area, volume, solid angles subtended by the polyhedron at its vertices, dihedral angles between the adjacent right kite faces etc. These formula are very useful for the analysis, modeling & designing of various uniform polyhedrons.
Tags:
Table , Trapezohedrons , Uniform
By:
harishchandraraj
Education
59 months ago
Download

Mathematical Analysis of Uniform Polyhedron (Trapezohedron) by HCR
The generalized formula are applicable on any uniform polyhedron having 2n congruent right kite faces, 4n edges & 2n+2 vertices lying on a spherical surface with a certain radius. These formula have been derived by the author Mr H.C. Rajpoot to analyse infinite no. of the uniform polyhedrons having congruent right kite faces simply by setting n=3,4,5,6,7,………………upto infinity, to calculate all the important parameters such as ratio of unequal edges, outer radius, inner radius, mean radius, surface area, volume, solid angles subtended by the polyhedron at its vertices, dihedral angles between the adjacent right kite faces etc. These formula are very useful for the analysis, modeling & designing of various uniform polyhedrons.
Tags:
Analysis , Congruent , Faces , Kite , Mathematical
By:
harishchandraraj
Education
59 months ago
Download

Table of solid angles subtended by Archimedean solids by HCR
Table of solid angles subtended at the vertices by all 13 Archimedean solids (uniform polyhedrons) calculated by the author Mr H.C. Rajpoot by using standard formula of solid angle & formula of tetrahedron. These are the standard values of solid angles which are useful for the analysis of all 13 Archimedean solids truncated tetrahedron, truncated hexahedron (cube), truncated octahedron, truncated dodecahedron, truncated icosahedron, cuboctahedron, icosidodecahedron, small rhombicuboctahedron, small rhombicosidodecahedron, snub cube, snub dodecahedron, great rhombicuboctahedron & great rhombicosidodecahedron.
Tags:
Angles , Archimedean , HCR , Polyhedrons , Solid
By:
harishchandraraj
Education
59 months ago
Download


Mathematical Analysis of Tetrahedron (solid angle by tetrahedron)
All the articles have been derived by the author Mr H.C. Rajpoot by using HCR's Inverse cosine formula & HCR's Theory of Polygon. These formula are very practical & simple to apply in case of any tetrahedron to calculate the internal (dihedral) angles between the consecutive lateral faces meeting at any of four vertices & the solid angle subtended by it (tetrahedron) at the vertex when the angles between the consecutive edges meeting at the same vertex are known. These are the generalized formula which can also be applied in case of three faces meeting at the vertex of various regular & uniform polyhedrons to calculate the solid angle subtended by polyhedron at its vertex.
Tags:
Analysis , Application , HCR , Mathematical , Polygon
By:
harishchandraraj
Education
59 months ago
Download

Data tables for dihedral angles of uniform polyhedral shells by HCR
These tables have been prepared by the author Mr H.C. Rajpoot by using his data tables of the various polyhedra for determining the dihedral angle between any two adjacent faces with a common edge of different uniform polyhedra or polyhedral shells. These are very useful for the construction & preparing the wireframe models of the uniform polyhedral shells having different regular polygonal faces. A polyhedral shell can be easily constructed/framed by continuously fixing all its adjacent (flat) faces each two as a pair at their common edge at an angle equal to the dihedral angle between them. These tables are very useful in analysis, designing & modeling of various uniform polyhedrons.
Tags:
Angles , Data , Dihedral , HCR , Polyhedra
By:
harishchandraraj
Education
60 months ago
Download

Table of the important parameters of uniform polyhedra by HCR
Table of the formula generalized by the author which are applicable to calculate the important parameters, of any uniform polyhedron having 2 congruent regular ngonal faces, 2n congruent trapezoidal faces each with three equal sides, 5n edges & 3n vertices lying on a spherical surface, such as solid angle subtended by each face at the centre, normal distance of each face from the centre, inner radius, outer radius, mean radius, surface area & volume. These are useful for analysis, designing & modeling of different uniform polyhedra.
Tags:
No tags for this presentation
By:
harishchandraraj
Education
60 months ago
Download

Mathematical Analysis of Uniform Polyhedra by HCR
All the formula are generalized by the author which are applicable to calculate the important parameters, of any uniform polyhedron having 2 congruent regular ngonal faces, 2n congruent trapezoidal faces each with three equal sides, 5n edges & 3n vertices lying on a spherical surface, such as solid angle subtended by each face at the centre, normal distance of each face from the centre, inner radius, outer radius, mean radius, surface area & volume. These are useful for analysis, designing & modeling of different uniform polyhedra.
Tags:
No tags for this presentation
By:
harishchandraraj
Education
60 months ago
Download
