File:Octaedro TD de Luis Abinader.gif
Octaedro_TD_de_Luis_Abinader.gif (479 × 367 pixels, file size: 3.81 MB, MIME type: image/gif, looped, 224 frames, 19 s)
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Español: Octaedro TD de Luis Abinader: Es un politopo tridimensional convexo de caras uniformes, posee 48 caras triangulares escalenas uniformes, 26 vértices deformes y 72 aristas deformes. Pertenece a la familia de poliedro convexo de caras uniformes.
Aplicando las fórmulas de sucesiones poliédricas triangulares, A=3L+3, C=2L+2, V=L+3, este poliedro posee 26 vértices, determinando el valor de L. V=26 sustituyendo y resolviendo formula. L=V-3= (26)-3=26-3=23. L=23, Sustituyendo el valor de L. A=3L+3=3(23)+3=69+3=72, este poliedro posee 72 aristas.. C=2L+2= 2(23)+2=46+2=48, este poliedro posee 48 aristas. Hemos comprobado que las fórmulas de las sucesiones poliédricas triangulares se cumplen en este poliedro. DATOS HISTÓRICOS DEL OCTAEDRO TD DE LUIS ABINADER A la 1:40 de a madrugada del 12 de enero del 2021, el descubridor de este solido geométrico, lo nombro con el nombre de Octaedro TD de Luis Abinader, en honor al presidente de la republica dominicana, Luis Abinader, esto fue debido al gran esfuerzo a favor de la clase humilde, que está haciendo el presidente, para controlar el covid 19, en la republica Dominicana. COORDENADAS CARTESIANAS DEL OCTAEDRO TD DE LUIS ABINADER. Los primeros seis vértices determinan un octaedro perfecto: A (-2, 0, 0) B (2, 0,0) C (0, 2, 0) D (0,-2, 0) E (0, 0, 2) F (0, 0, -2). Posee 8 caras que son triangulos equilateros uniformes. Si combinamos estos 12 puntos, desde el vértice (G), hasta el Vértice (R) obtenemos uno de los poliedros de Arquímedes llamado cuboctaedro: G (1.2, 0, 1.2) H (-1.2, 0, 1.2) I (0,-1.2, 1.2) J (0, 1.2, 1.2) K (1.2, 0, -1.2) L (-1.2, 0, -1.2) M (0,-1.2, -1.2) N (0, 1.2, -1.2) O (1.2, 1.2, 0) P (1.2, -1.2, 0) Q (-1.2, 1.2, 0) R (-1.2, -1.2, 0). Combinando los últimos 12 puntos, desde el vértice (s), hasta el vértice (B1), obtendremos un cubo perfecto. S (1, 1, 1) T (1, -1, 1) U (-1, 1, 1) V (-1, -1, 1) W (1, 1, -1) Z (1, -1, -1) A1 (-1, 1, -1) B1 (-1, -1, -1). Combinando estos puntos:A (-2, 0, 0) B (2, 0,0) C (0, 2, 0) D (0,-2, 0) E (0, 0, 2) F (0, 0, -2) + S (1, 1, 1) T (1, -1, 1) U (-1, 1, 1) V (-1, -1, 1) W (1, 1, -1) Z (1, -1, -1) A1 (-1, 1, -1) B1 (-1, -1, -1). Obtendremos unos de los poliedros de catalán llamado Triquisoctaedro, que posee 24 triángulos isósceles. Combinando estos 26 vértices: A (-2, 0, 0) B (2, 0,0) C (0, 2, 0) D (0,-2, 0) E (0, 0, 2) F (0, 0, -2) + G (1.2, 0, 1.2) H (-1.2, 0, 1.2) I (0,-1.2, 1.2) J (0, 1.2, 1.2) K (1.2, 0, -1.2) L (-1.2, 0, -1.2) M (0,-1.2, -1.2) N (0, 1.2, -1.2) O (1.2, 1.2, 0) P (1.2, -1.2, 0) Q (-1.2, 1.2, 0) R (-1.2, -1.2, 0) + S (1, 1, 1) T (1, -1, 1) U (-1, 1, 1) V (-1, -1, 1) W (1, 1, -1) Z (1, -1, -1) A1 (-1, 1, -1) B1 (-1, -1, -1). Obtendremos unos de los poliedros del profesor Jose Joel Leonardo, llamado octaedro triakis duplo de Luis Abinader, dado a conocer con el nombre simplicado de octaedro TD de Luis abinader.English: Octahedron TD by Luis Abinader: It is a convex three-dimensional polytope with uniform faces, it has 48 uniform scalen triangular faces, 26 deformed vertices and 72 deformed edges. It belongs to the family of convex polyhedron with uniform faces.
Applying the formulas of triangular polyhedral sequences, A = 3L + 3, C = 2L + 2, V = L + 3, this polyhedron has 26 vertices, determining the value of L. V = 26 by substituting and solving the formula. L = V-3 = (26) -3 = 26-3 = 23. L = 23, Substituting the value of L. A = 3L + 3 = 3 (23) + 3 = 69 + 3 = 72, this polyhedron has 72 edges. C = 2L + 2 = 2 (23) + 2 = 46 + 2 = 48, this polyhedron has 48 edges. We have verified that the formulas of the triangular polyhedral sequences are fulfilled in this polyhedron. HISTORICAL DATA OF LUIS ABINADER'S OCTAEDRO TD At 1:40 in the morning of January 12, 2021, the discoverer of this geometric solid named it with the name Octaedro TD de Luis Abinader, in honor of the president of the Dominican Republic, Luis Abinader, this was due to the great effort in favor of the humble class, which the president is making, to control covid 19, in the Dominican Republic. CARTESIAN COORDINATES OF THE OCTAEDRO TD OF LUIS ABINADER. The first six vertices determine a perfect octahedron: A (-2, 0, 0) B (2, 0,0) C (0, 2, 0) D (0, -2, 0) E (0, 0, 2 ) F (0, 0, -2). It has 8 faces that are uniform equilateral triangles. If we combine these 12 points, from the vertex (G), to the vertex (R) we obtain one of the Archimedean polyhedra called a cuboctahedron: G (1.2, 0, 1.2) H (-1.2, 0, 1.2) I (0, -1.2, 1.2) J (0, 1.2, 1.2) K (1.2, 0, -1.2) L (-1.2, 0, -1.2) M (0, -1.2, -1.2) N (0, 1.2, -1.2 ) O (1.2, 1.2, 0) P (1.2, -1.2, 0) Q (-1.2, 1.2, 0) R (-1.2, -1.2, 0). Combining the last 12 points, from the vertex (s), to the vertex (B1), we will obtain a perfect cube. S (1, 1, 1) T (1, -1, 1) U (-1, 1, 1) V (-1, -1, 1) W (1, 1, -1) Z (1, - 1, -1) A1 (-1, 1, -1) B1 (-1, -1, -1). Combining these points: A (-2, 0, 0) B (2, 0,0) C (0, 2, 0) D (0, -2, 0) E (0, 0, 2) F (0, 0, -2) + S (1, 1, 1) T (1, -1, 1) U (-1, 1, 1) V (-1, -1, 1) W (1, 1, -1 ) Z (1, -1, -1) A1 (-1, 1, -1) B1 (-1, -1, -1). We will obtain one of the Catalan polyhedra called Triquisoctahedron, which has 24 isosceles triangles. Combining these 26 vertices: A (-2, 0, 0) B (2, 0,0) C (0, 2, 0) D (0, -2, 0) E (0, 0, 2) F (0 , 0, -2) + G (1.2, 0, 1.2) H (-1.2, 0, 1.2) I (0, -1.2, 1.2) J (0, 1.2, 1.2) K (1.2, 0, -1.2) L (-1.2, 0, -1.2) M (0, -1.2, -1.2) N (0, 1.2, -1.2) O (1.2, 1.2, 0) P (1.2, -1.2, 0) Q (-1.2 , 1.2, 0) R (-1.2, -1.2, 0) + S (1, 1, 1) T (1, -1, 1) U (-1, 1, 1) V (-1, -1, 1) W (1, 1, -1) Z (1, -1, -1) A1 (-1, 1, -1) B1 (-1, -1, -1). We will obtain one of the polyhedra of Professor Jose Joel Leonardo, called the double triakis octahedron of Luis Abinader, made known with the simplified name of the TD octahedron of Luis abinader.Français : Octaèdre TD de Luis Abinader: C'est un polytope tridimensionnel convexe avec des faces uniformes, il a 48 faces triangulaires scalaires uniformes, 26 sommets déformés et 72 arêtes déformées. Il appartient à la famille des polyèdres convexes à faces uniformes.
En appliquant les formules des séquences polyédriques triangulaires, A = 3L + 3, C = 2L + 2, V = L + 3, ce polyèdre a 26 sommets, déterminant la valeur de L. V = 26 en substituant et en résolvant la formule. L = V-3 = (26) -3 = 26-3 = 23. L = 23, en remplaçant la valeur de L. A = 3L + 3 = 3 (23) + 3 = 69 + 3 = 72, ce polyèdre a 72 arêtes. C = 2L + 2 = 2 (23) + 2 = 46 + 2 = 48, ce polyèdre a 48 arêtes. Nous avons vérifié que les formules des séquences polyédriques triangulaires sont remplies dans ce polyèdre. DONNÉES HISTORIQUES DE L'OCTAEDRO TD DE LUIS ABINADER A 1h40 du matin du 12 janvier 2021, le découvreur de ce solide géométrique l'a baptisé du nom d'Octaedro TD de Luis Abinader, en l'honneur du président de la République dominicaine, Luis Abinader, cela était dû au grand effort en faveur de la classe humble, que fait le président, pour contrôler le covid 19, en République dominicaine. COORDONNÉES CARTESIENNE DE L'OCTAEDRO TD DE LUIS ABINADER. Les six premiers sommets déterminent un octaèdre parfait: A (-2, 0, 0) B (2, 0,0) C (0, 2, 0) D (0, -2, 0) E (0, 0, 2 ) F (0, 0, -2). Il a 8 faces qui sont des triangles équilatéraux uniformes. Si nous combinons ces 12 points, du sommet (G), au sommet (R), nous obtenons l'un des polyèdres d'Archimède appelé cuboctaèdre: G (1,2, 0, 1,2) H (-1,2, 0, 1,2) I (0, -1,2, 1,2) J (0, 1,2, 1,2) K (1,2, 0, -1,2) L (-1,2, 0, -1,2) M (0, -1,2, -1,2) N (0, 1,2, -1,2 ) O (1,2, 1,2, 0) P (1,2, -1,2, 0) Q (-1,2, 1,2, 0) R (-1,2, -1,2, 0). En combinant les 12 derniers points, du (des) sommet (s), au sommet (B1), nous obtiendrons un cube parfait. S (1, 1, 1) T (1, -1, 1) U (-1, 1, 1) V (-1, -1, 1) W (1, 1, -1) Z (1, - 1, -1) A1 (-1, 1, -1) B1 (-1, -1, -1). En combinant ces points: A (-2, 0, 0) B (2, 0,0) C (0, 2, 0) D (0, -2, 0) E (0, 0, 2) F (0, 0, -2) + S (1, 1, 1) T (1, -1, 1) U (-1, 1, 1) V (-1, -1, 1) W (1, 1, -1 ) Z (1, -1, -1) A1 (-1, 1, -1) B1 (-1, -1, -1). Nous obtiendrons l'un des polyèdres catalans appelé Triquisoctaèdre, qui comporte 24 triangles isocèles. Combinant ces 26 sommets: A (-2, 0, 0) B (2, 0,0) C (0, 2, 0) D (0, -2, 0) E (0, 0, 2) F (0 , 0, -2) + G (1,2, 0, 1,2) H (-1,2, 0, 1,2) I (0, -1,2, 1,2) J (0, 1,2, 1,2) K (1,2, 0, -1,2) L (-1,2, 0, -1,2) M (0, -1,2, -1,2) N (0, 1,2, -1,2) O (1,2, 1,2, 0) P (1,2, -1,2, 0) Q (-1,2 , 1,2, 0) R (-1,2, -1,2, 0) + S (1, 1, 1) T (1, -1, 1) U (-1, 1, 1) V (-1, -1, 1) W (1, 1, -1) Z (1, -1, -1) A1 (-1, 1, -1) B1 (-1, -1, -1). Nous obtiendrons l'un des polyèdres du professeur Jose Joel Leonardo, appelé l'octaèdre double triakis de Luis Abinader, connu sous le nom simplifié de l'octaèdre TD de Luis abinader. |
| Date | |
| Source | Own work |
| Author | Jose J. Leonard |
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