Mathematical Analysis of Truncated Tetrahedron
All the important parameters of a truncated tetrahedron such as normal distances & solid angles subtended by the faces, inner radius, outer radius, mean radius, surface area & volume have been calculated by using HCR's formula for regular polyhedron. This formula is a generalized dimensional formula which is applied on any of the five platonic solids i.e. reguler tetrahedron, regular hexahedron (cube), regular octahedron, regular dodecahedron & regular icosahedron to calculate their important parameters. It can be used in analysis, designing & modelling of regular npolyhedrons.
Tags:
Analysis , Mathematical , TETRAHEDRON , Truncated
By:
harishchandraraj
Science & Technology
60 months ago
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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
57 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
60 months ago
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Volume of tetrahedron bounded by a given plane & the coordinate planes
The article here deals with the derivation of a general expression to calculate the volume of tetrahedron/pyramid bounded by a given plane & the coordinate planes (i.e. XYplane, YZplane & ZXplane) using intercept form of equation of a plane in 3D space. All the derivations are based on simple geometry. These are very useful to directly calculate the volume of the bounded tetrahedron/pyramid.
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By:
harishchandraraj
Education
50 months ago
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Mathematical analysis of Disphenoid (isosceles tetrahedron) by HCR
The author Mr H.C. Rajpoot has derived the formula to analytically compute all the important parameters of a disphenoid (isosceles tetrahedron with four congruent acutetriangular faces) such as volume, surface area, vertical height, radii of inscribed & circumscribed spheres, solid angle subtended at each vertex, coordinates of vertices, incentre, circumcentre & centroid of a disphenoid for the optimal configuration in 3D space. The author has also proved the important conclusions related to a disphenoid by mathematical derivations using 3D coordinate geometry.
Tags:
Circumradius , Disphenoid , Isosceles , TETRAHEDRON , Volume and
By:
harishchandraraj
Education
31 months ago
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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
56 months ago
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HCR's Inverse Cosine Formula (Analysis of intersecting planes)
HCR’s Inverse Cosine Formula derived by Mr H.C. Rajpoot is a trigonometric relation of four variables/angles. It is applicable for any three straight lines or planes, either coplanar or noncoplanar, intersecting each other at a single point in the space. It directly corelates the internal angles (i.e. angles between the consecutive lateral faces) & the face angles (i.e. angles between the consecutive lateral edges) of any tetrahedron. This formula is very useful to find out all the unknown internal angles if all the face angles of any tetrahedron are known & vice versa.
Tags:
HCR , HCRs Inverse cosine form , Verse cosine formula
By:
harishchandraraj
Celebrities
60 months ago
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