
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
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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
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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
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All the important parameters of a truncated icosahedron
All the important parameters of a truncated icosahedron (Goldberg polyhedron, G(1,1)) such as normal distances & solid angles of the faces, inner radius, outer radius, mean radius, surface area & volume have been calculated by using HCR's formula for regular polyhedrons (all five platonic solids)
Tags:
Goldbergpolyhedron , HCRsFormula , HCRsTheory of Polygon , Icosahedron , Truncated
By:
harishchandraraj
Science & Technology
62 months ago
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All the important parameters of an icosidodecahedron by HCR
Table of all the important parameters of an icosidodecahedron (having 20 congruent equilateral triangular & 12 congruent regular pentagonal faces each of equal edge length) such as normal distances & solid angles subtended by the faces, inner radius, outer radius, mean radius, surface area & volume calculated by using HCR's formula for regular polyhedrons. It can be used in analysis, designing & modelling of polyhedrons.
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By:
harishchandraraj
Science & Technology
62 months ago
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All the important parameters of a truncated tetrahedron
Table of all the important parameters of a truncated tetrahedron (having 4 congruent equilateral triangular & 4 congruent regular hexagonal faces each of equal edge length) such as normal distances & solid angles subtended by the faces, inner radius, outer radius, mean radius, surface area & volume calculated by using HCR's formula for regular polyhedrons. It can be used in analysis, designing & modelling of polyhedrons.
Tags:
Table , TETRAHEDRON , Truncated
By:
harishchandraraj
Education
62 months ago
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All the important parameters of a truncated cuboctahedron
Table of the important parameters of a truncated cuboctahedron (having 8 congruent equilateral triangular, 6 congruent square & 12 congruent golden rectangular faces) such as normal distances & solid angles subtended by the faces, inner radius, outer radius, mean radius, surface area & volume calculated by using HCR's formula for regular polyhedrons. It can be used in analysis, designing & modelling of polyhedrons.
Tags:
Cuboctahedron , GOLDEN , Rectangles , Table , Truncated
By:
harishchandraraj
Education
61 months ago
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All the important parameters of a truncated icosidodecahedron
Table of all the important parameters of a truncated icosidodecahedron (having 20 congruent equilateral triangular faces, 30 congruent golden rectangular faces & 12 congruent regular pentagonal faces) such as normal distances & solid angles subtended by the faces, inner radius, outer radius, mean radius, surface area & volume calculated by using HCR's formula for regular polyhedrons. It can be used in analysis, designing & modelling of polyhedrons.
Tags:
GOLDEN , Icosidodecahedron , Rectangles , Table , Truncated
By:
harishchandraraj
Education
62 months ago
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