File:Tetraedro de Pacheco Ampliado.gif
Tetraedro_de_Pacheco_Ampliado.gif (495 × 402 pixels, file size: 2.15 MB, MIME type: image/gif, looped, 174 frames, 13 s)
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Español: Tetraedro de Pacheco ampliado: es un poliedro convexo que posee 14 vértices, 36 aristas no uniformes y 24 caras triangulares escalenas que son iguales entre sí.
Esta variedad se distingue porque las altura de la pirámides que lo componen son lo más elevada posible, siempre y cuando el poliedro pueda conservar, las características de caras, vértices y aristas que lo distinguen. Acorde con el matemático dominicano Jose Joel Leonardo, el tetraedro ampliado de pacheco es uno de los poliedros que complementa, la familia de los poliedros de catalán, que fueron descubiertos por el matemático belga Eugéne Charles Catalán. Este poliedro posee dos clase de vértices: Ochos vértices donde coinciden seis triángulos escalenos congruentes y seis vértices donde coinciden cuatro triángulos escalenos uniformes, para un total de 14 vértices. El conjunto de los 14 vértices que definen el tetraedro de pacheco están representados por estos catorces tríos cartesianos: A (5, 2.886751345948129, -2.041241452319315), B (-5, 2.886751345948129, -2.041241452319315), C (0, -5.773502691896258, -2.041241452319315), D (0, 0, 6.123724356957946), E (3.467674342361211, 2.002062715024204, 2.83134424430873), F (-3.467674342361211, 2.002062715024204, 2.83134424430873), G (0, -4.004125430048408, 2.83134424430873), H (-3.467674342361211, -2.002062715024204, -2.83134424430873), I (3.467674342361211, -2.002062715024204, -2.83134424430873), J (0, 4.004125430048408, -2.83134424430873), K (3.853147837178333,-2.224615941022336,1.573041017432586), L (-3.853147837178333, -2.224615941022336, 1.573041017432586), M (0,4.449231882044669,1.573041017432586), y el punto N (0,0,-4.719123052297758). Este poliedro posee una precisión de base 10 elevada a potencia -13 y los colores del primer diseño del tetraedro de pacheco ampliado, representan los colores básicos de la bandera dominicana.English: Tetrahedron of Pacheco expanded: it is a convex polyhedron that has 14 vertices, 36 non-uniform edges and 24 scaled triangular faces that are equal to each other.
This variety is distinguished because the height of the pyramids that compose it are as high as possible, as long as the polyhedron can preserve the characteristics of faces, vertices and edges that distinguish it. According to the Dominican mathematician Jose Joel Leonardo, the expanded tetrahedron of Pacheco is one of the polyhedra that complements the family of Catalan polyhedra, which were discovered by the Belgian mathematician Eugéne Charles Catalán. This polyhedron has two kinds of vertices: Eight vertices where six congruent scalene triangles coincide and six vertices where four uniform scalene triangles coincide, for a total of 14 vertices. The set of 14 vertices that define the tetrahedron of Pacheco are represented by these fourteen Cartesian triplets: A (5, 2.886751345948129, -2.041241452319315), B (-5, 2.886751345948129, -2.041241452319315), C (0, -.04124157319315), C (0, -.0415445948129) ), D (0, 0, 6.123724356957946), E (3.467674342361211, 2.002062715024204, 2.83134424430873), F (-3.467674342361211, 2.002062715024204, 2.83134424430873), G (0, -4.004125430048408, 2.83134424430873), H (-3.467674342361211, -2.002062715024204, -2.83134424430873 ), I (3.467674342361211, -2.002062715024204, -2.83134424430873), J (0, 4.004125430048408, -2.83134424430873), K (3.853147837178333, -2.224615941022336,1.573041017432586), L (-3.853147837178333, -2.224615941022336, 1.573041017432586), M (0,4.449231882044669, 1.573041017432586), and point N (0.0, -4.719123052297758). This polyhedron has a precision of base 10 raised to power -13 and the colors of the first design of the expanded Pacheco tetrahedron represent the basic colors of the Dominican flag.Français : Tétraèdre de Pacheco développé: c'est un polyèdre convexe qui a 14 sommets, 36 arêtes non uniformes et 24 faces triangulaires échelonnées qui sont égales les unes aux autres.
Cette variété se distingue car la hauteur des pyramides qui la composent est la plus élevée possible, à condition que le polyèdre puisse conserver les caractéristiques des faces, des sommets et des arêtes qui la distinguent. Selon le mathématicien dominicain Jose Joel Leonardo, le tétraèdre expansé de Pacheco est l'un des polyèdres qui complète la famille des polyèdres catalans, qui ont été découverts par le mathématicien belge Eugéne Charles Catalán. Ce polyèdre a deux types de sommets: huit sommets où six triangles scalènes congruents coïncident et six sommets où quatre triangles scalènes uniformes coïncident, pour un total de 14 sommets. L'ensemble des 14 sommets qui définissent le tétraèdre de Pacheco sont représentés par ces quatorze triplets cartésiens: A (5, 2.886751345948129, -2.041241452319315), B (-5, 2.886751345948129, -2.041241452319315), C (0, -.04484157319315), C (0, -.04484157319315), C (0, -.0448) ), D (0, 0, 6,123724356957946), E (3,467674342361211, 2,002062715024204, 2,83134424430873), F (-3,467674342361211, 2,002062715024204, 2,83134424430873), G (0, -4,004125430048408, 2,83134424430873), H (-3,467674342361211, -2,002062715024204, -2,83134424430873 ), I (3,467674342361211, -2,002062715024204, -2,83134424430873), J (0, 4,004125430048408, -2,83134424430873), K (3,853147837178333, -2.224615941022336,1.573041017432586), L (-3,853147837178333, -2,224615941022336, 1,573041017432586), M (0,4.449231882044669, 1,573041017432586) et le point N (0,0, -4,719123052297758). Ce polyèdre a une précision de base 10 élevée à la puissance -13 et les couleurs du premier dessin du tétraèdre Pacheco expansé représentent les couleurs de base du drapeau dominicain. Más información sobre este texto de origenPara obtener más información sobre la traducción, se necesita el texto de origen Enviar comentarios Paneles laterales |
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| Source | Own work |
| Author | Jose J. Leonard |
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