Added: Apr 03, 2015 | |

By: harishchandraraj | |

Views: 150 | |

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. |

Added: Dec 11, 2014 | |

By: harishchandraraj | |

Views: 79 | |

This formula was derived by H.C. Rajpoot to calculate all the important parameters of a regular n-polyhedron such as inner radius, outer radius, mean radius, surface area & volume. This formula is a generalized dimensional formula which can be applied on any existing n-polyhedron since it depends on two parameters of any regular polyhedron as the no. of faces & the no. of edges in one face only. It can be used in analysis, designing & modelling of regular n-polyhedrons. |

Added: Jun 07, 2015 | |

By: harishchandraraj | |

Views: 53 | |

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 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 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. |

Added: Jun 07, 2015 | |

By: harishchandraraj | |

Views: 25 | |

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 n-gonal 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. |