File:Hexaedro Ultra Leonardiano.gif
Hexaedro_Ultra_Leonardiano.gif (389 × 399 pixels, file size: 1.2 MB, MIME type: image/gif, looped, 70 frames, 5.5 s)
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Español: El hexaedro ultra Leonardiano: Es un politopo tridimensional cóncavo irregular, que posee 72 caras interiores y 144 caras ultra interiores para un total de 216 caras. Tiene 24 aristas exteriores, 144 aristas interiores, 72 arista ultra interiores, 72 arista ultra exteriores y 12 aristas intermedias, para un total de 324 aristas. Además, ostenta 6 vértices exteriores, 24 vértices ultra exteriores, 72 vértices interiores y 8 vértices intermedios para un total de 110 vértices. Este poliedro fue descubierto el 10 de mayo del 2010, por el dominicano, José Joel Leonardo. Pertenece al grupo de los poliedros estrellado ultra hueco.
Si aplicamos la fórmula de poliedro de Euler, C+V-A=2, sustituyendo C=216, A=324, V=110, procedemos 216+110-324= 326-324=2, la formula se cumple. Si aplicamos las fórmulas de Sucesiones poliédricas triangulares de Leonardo, tenemos A=3L+3, C=2L+2, V=L+3, si V=110 entonces despejamos el valor de la variable L. L= V-3, sustituyendo L=110 -3 = 107. El valor de la variable L= 107. Si sustituimos el valor de L= 107 en la fórmula: A= 3L+3 =3(107)+3=321+3= 324, por lo tanto A= 324. Si sustituimos el valor de L= 107 en la fórmula: C=2L+2= 2(107)+2= 214+2= 216, por lo tanto C=216. Con la variable (L) determinamos la posición del orden numérico natural al que corresponde cada poliedro que posee todas sus caras en forma de triángulos. El conjunto de los vértices exteriores del hexaedro ultra Leonardiano, forman perfectamente un octaedro regular imaginario. La sexta estelación del hexaedro está representada por dos variedades fundamentales de este politopo tridimensional, los cuales son: el Hexaedro Ultra Leonardiano y Hexaedro Ultra Leonardiano ampliado.English: The ultra Leonardian hexahedron: It is an irregular concave three-dimensional polytope, which has 72 inner faces and 144 ultra inner faces for a total of 216 faces. It has 24 exterior edges, 144 interior edges, 72 ultra interior edges, 72 ultra exterior edges and 12 intermediate edges, for a total of 324 edges. In addition, it boasts 6 exterior vertices, 24 ultra exterior vertices, 72 interior vertices and 8 intermediate vertices for a total of 110 vertices. This polyhedron was discovered on May 10, 2010, by the Dominican, José Joel Leonardo. It belongs to the group of ultra hollow star polyhedra.
If we apply Euler's polyhedron formula, C + V-A = 2, substituting C = 216, A = 324, V = 110, we proceed 216 + 110-324 = 326-324 = 2, the formula is fulfilled. If we apply Leonardo's triangular polyhedral succession formulas, we have A = 3L + 3, C = 2L + 2, V = L + 3, if V = 110 then we clear the value of the variable L. L = V-3, substituting L = 110 -3 = 107. The value of the variable L = 107. If we substitute the value of L = 107 in the formula: A = 3L + 3 = 3 (107) + 3 = 321 + 3 = 324, therefore A = 324. If we substitute the value of L = 107 in the formula: C = 2L + 2 = 2 (107) + 2 = 214 + 2 = 216, therefore C = 216. With the variable (L) we determine the position of the natural numerical order to which each polyhedron that has all its faces in the form of triangles corresponds. The set of the outer vertices of the ultra Leonardian hexahedron perfectly form an imaginary regular octahedron. The sixth stelation of the hexahedron is represented by two fundamental varieties of this three-dimensional polytope, which are: the Ultra Leonardian Hexahedron and Extended Ultra Leonardian Hexahedron.Français : Hexaèdre ultra léonardien: il s'agit d'un polytope tridimensionnel concave irrégulier, qui a 72 faces internes et 144 faces ultra internes pour un total de 216 faces. Il a 24 bords extérieurs, 144 bords intérieurs, 72 bords ultra intérieurs, 72 bords ultra extérieurs et 12 bords intermédiaires, pour un total de 324 bords. De plus, il possède 6 sommets extérieurs, 24 sommets ultra extérieurs, 72 sommets intérieurs et 8 sommets intermédiaires pour un total de 110 sommets. Ce polyèdre a été découvert le 10 mai 2010 par le dominicain José Joel Leonardo. Il appartient au groupe des polyèdres étoilés ultra creux.
Si nous appliquons la formule du polyèdre d'Euler, C + V-A = 2, en remplaçant C = 216, A = 324, V = 110, nous procédons 216 + 110-324 = 326-324 = 2, la formule est remplie. Si nous appliquons les formules de succession polyédrique triangulaire de Leonardo, nous avons A = 3L + 3, C = 2L + 2, V = L + 3, si V = 110 alors nous effaçons la valeur de la variable L. L = V-3, en remplaçant L = 110 -3 = 107. La valeur de la variable L = 107. Si nous substituons la valeur de L = 107 dans la formule: A = 3L + 3 = 3 (107) + 3 = 321 + 3 = 324, donc A = 324. Si nous substituons la valeur de L = 107 dans la formule: C = 2L + 2 = 2 (107) + 2 = 214 + 2 = 216, donc C = 216. Avec la variable (L) nous déterminons la position de l'ordre numérique naturel auquel correspond chaque polyèdre qui a toutes ses faces sous forme de triangles. L'ensemble des sommets extérieurs de l'hexaèdre ultra léonardien forme parfaitement un octaèdre régulier imaginaire. La sixième stèle de l'hexaèdre est représentée par deux variétés fondamentales de ce polytope tridimensionnel, qui sont: l'hexaèdre ultra léonardien et l'hexaèdre ultra léonardien étendu. |
| Date | |
| Source | Own work |
| Author | Jose J. Leonard |
https://www.geogebra.org/m/guye49wg https://commons.wikimedia.org/wiki/File:Sucesiones_Poliedricas_Triangulares.jpg https://commons.wikimedia.org/wiki/File:Sexta_Estelaci%C3%B3n_del_Cubo_o_Hexaedro.jpg
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| current | 23:29, 21 December 2019 | | 389 × 399 (1.2 MB) | Jose J. Leonard (talk | contribs) | User created page with UploadWizard |
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