


Mathematical Analysis of Truncated Octahedron
All the important parameters of a truncated octahedron 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 , Octahedron , Truncated
By:
harishchandraraj
Science & Technology
62 months ago
Download

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
62 months ago
Download



Mathematical Analysis of Icosidodecahedron by HCR
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 have been calculated by using HCR's formula for regular polyhedrons. 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 also be used in analysis, designing & modelling of truncated polyhedrons.
Tags:
No tags for this presentation
By:
harishchandraraj
Education
62 months ago
Download

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

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
