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Truncated Trapezohedra
In geometry, an truncated trapezohedron is a polyhedron formed by a trapezohedron with Pyramid (geometry), pyramids Truncation (geometry), truncated from its two polar axis Vertex (geometry), vertices. The vertices exist as 4 in four parallel planes, with alternating orientation in the middle creating the pentagons. The regular dodecahedron is the most common polyhedron in this class, being a Platonic solid, with 12 Congruence (geometry), congruent pentagonal faces. A truncated trapezohedron has all vertices with 3 faces. This means that the dual polyhedra, the set of gyroelongated dipyramids, have all triangular faces. For example, the icosahedron is the dual of the dodecahedron. Forms *Triangular truncated trapezohedron (Dürer's solid) – 6 pentagons, 2 triangles, dual gyroelongated triangular dipyramid *Truncated square trapezohedron – 8 pentagons, 2 squares, dual gyroelongated square dipyramid *''Truncated pentagonal trapezohedron'' or regular dodecahedron – 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regular Dodecahedron
A regular dodecahedron or pentagonal dodecahedronStrictly speaking, a pentagonal dodecahedron need not be composed of regular pentagons. The name "pentagonal dodecahedron" therefore covers a wider class of solids than just the Platonic solid, the regular dodecahedron. is a dodecahedron composed of regular polygon, regular pentagonal faces, three meeting at each Vertex (geometry), vertex. It is an example of Platonic solids, described as cosmic stellation by Plato in his dialogues, and it was used as part of Solar System proposed by Johannes Kepler. However, the regular dodecahedron, including the other Platonic solids, has already been described by other philosophers since antiquity. The regular dodecahedron is a truncated trapezohedron because it is the result of Truncation (geometry), truncating axial vertices of a pentagonal trapezohedron. It is also a Goldberg polyhedron because it is the initial polyhedron to construct new polyhedrons by the process of chamfering. It has a re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
