File:Estrella octaédrica Reina Isabel II.gif
Estrella_octaédrica_Reina_Isabel_II.gif (434 × 385 pixels, file size: 4.12 MB, MIME type: image/gif, looped, 200 frames, 13 s)
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Summary
[edit]DescriptionEstrella octaédrica Reina Isabel II.gif |
Español: Es un sólido tridimensional cóncavo, el cual está compuesto por 24 triángulos isósceles de Jose uniformes entre sí, 14 vértices y 36 aristas deformes. El poliedro dual de este solido es el cuboctaedro.
Los 14 vértices están distribuidos en: Ochos vértices exteriores los cuales son comunes a tres triángulos isósceles de Jose (M = (2.222222222222222, 1.283000598199168, 2.948459875572344), N = (0, 2.566001196398337, 1.134023029066286), O = (2.222222222222222, -1.283000598199168, 1.134023029066286), P = (0, -2.566001196398337, 2.948459875572344), Q = (-2.222222222222222, 1.283000598199168, 2.948459875572344), R = (-2.222222222222222, -1.283000598199168, 1.134023029066286), S = (0, 0, 4.762896722078402), T = (0, 0, -0.680413817439772)) y seis vértices intermedios, donde convergen ochos triángulos isósceles de Jose en cada uno de ellos (U = (1.6666666666666667, 0.962250448649377, 0.680413817439772), V = (0, 1.924500897298753, 3.402069087198859), W = (-1.6666666666666667, 0.962250448649376, 0.680413817439772), Z = (1.6666666666666667, -0.962250448649377, 3.402069087198859), A1 = (0, -1.924500897298753, 0.680413817439772), B1 = (-1.6666666666666667, -0.962250448649376, 3.402069087198859)). Las 36 aristas están distribuidas en doce aristas intermedias y 24 aristas exteriores estrelladas. Las aristas intermedias en este poliedro son de mayor medida que las aristas exteriores estrelladas. La dualidad entre la Estrella octaédrica Reina Isabel II y el cuboctaedro está demostrada en la definición de estos 26 puntos geométricos: A = (1.6666666666666667, 0.962250448649376, 4.762896722078402), B = (1.6666666666666667, 2.886751345948129, 2.041241452319315), C = (-1.6666666666666667, 2.886751345948129, 2.041241452319315), D = (3.3333333333333335, 0, 2.041241452319315), E = (0, -1.924500897298752, 4.762896722078402), F = (1.6666666666666667, -2.886751345948129, 2.041241452319315), G = (-1.6666666666666667, -2.886751345948129, 2.041241452319315), H = (-1.6666666666666667, 0.962250448649376, 4.762896722078402), I = (-3.3333333333333335, 0, 2.041241452319315), J = (0, 1.924500897298753, -0.680413817439772), K = (-1.6666666666666667, -0.962250448649376, -0.680413817439772), L = (1.6666666666666667, -0.962250448649376, -0.680413817439772), M = (2.222222222222222, 1.283000598199168, 2.948459875572344), N = (0, 2.566001196398337, 1.134023029066286), O = (2.222222222222222, -1.283000598199168, 1.134023029066286), P = (0, -2.566001196398337, 2.948459875572344), Q = (-2.222222222222222, 1.283000598199168, 2.948459875572344), R = (-2.222222222222222, -1.283000598199168, 1.134023029066286), S = (0, 0, 4.762896722078402), T = (0, 0, -0.680413817439772), U = (1.6666666666666667, 0.962250448649377, 0.680413817439772), V = (0, 1.924500897298753, 3.402069087198859), W = (-1.6666666666666667, 0.962250448649376, 0.680413817439772), Z = (1.6666666666666667, -0.962250448649377, 3.402069087198859), A1 = (0, -1.924500897298753, 0.680413817439772), B1 = (-1.6666666666666667, -0.962250448649376, 3.402069087198859). Este politopo tridimensional fue descubierto por el Dominicano Jose Joel Leonardo el 4 de enero del 2020 a las 8:18 Pm y fue nombrado por su autor el 16 de enero del 2021 en honor a la reina de Inglaterra Isabel II. Los primeros 12 puntos definen un cuboctaedro de Arquímedes (desde el punto A, hasta el punto L). Los 14 puntos restantes definen los puntos medios de cada una de las caras que forman el cuboctaedro (desde el punto M, hasta el punto B1) y con la combinación de estos catorces puntos formamos la Estrella octaédrica Reina Isabel II.English: It is a three-dimensional concave solid, which is composed of 24 isosceles triangles of Jose uniform with each other, 14 vertices and 36 deformed edges. The dual polyhedron of this solid is the cuboctahedron.
14 vertices are distributed in: Eight outer vertices which are common to three isosceles triangles Jose (M = (2.222222222222222, 1.283000598199168, 2.948459875572344), N = (0, 2.566001196398337, 1.134023029066286), O = (2.222222222222222, -1.283000598199168, 1.134023029066286 ), P = (0, -2.566001196398337, 2.948459875572344), Q = (-2.222222222222222, 1.283000598199168, 2.948459875572344), R = (-2.222222222222222, -1.283000598199168, 1.134023029066286), S = (0, 0, 4.762896722078402), T = (0 , 0, -0.680413817439772)) and six intermediate vertices where eight isosceles triangles converge Jose in each (U = (1.6666666666666667, 0.962250448649377, 0.680413817439772), V = (0, 1.924500897298753, 3.402069087198859), W = (-1.6666666666666667 , 0.962250448649376, 0.680413817439772), Z = (1.6666666666666667, -0.962250448649377, 3.402069087198859) A1 = (0, -1.924500897298753, 0.680413817439772), B1 = (-1.6666666666666667, -0.962250448649376, 3.402069087198859)). The 36 edges are distributed in twelve intermediate edges and 24 outer star edges. The intermediate edges in this polyhedron are larger than the outer stellate edges. The duality between the octahedral Star Queen Isabel II and cuboctahedron is demonstrated in defining these 26 geometric points A = (1.6666666666666667, 0.962250448649376, 4.762896722078402), B = (1.6666666666666667, 2.886751345948129, 2.041241452319315), C = (-1.6666666666666667, 2.886751345948129 , 2.041241452319315), D = (3.3333333333333335, 0, 2.041241452319315), E = (0, -1.924500897298752, 4.762896722078402), F = (1.6666666666666667, -2.886751345948129, 2.041241452319315), G = (-1.6666666666666667, -2.886751345948129, 2.041241452319315), H = (-1.6666666666666667, 0.962250448649376, 4.762896722078402), I = (-3.3333333333333335, 0, 2.041241452319315), J = (0, 1.924500897298753, -0.680413817439772), K = (-1.6666666666666667, -0.962250448649376, -0.680413817439772), L = (1.6666666666666667, - 0.962250448649376, -0.680413817439772), M = (2.222222222222222, 1.283000598199168, 2.948459875572344), N = (0, 2.566001196398337, 1.134023029066286), O = (2.222222222222222, -1.283000598 199168, 1.134023029066286), P = (0, -2.566001196398337, 2.948459875572344), Q = (-2.222222222222222, 1.283000598199168, 2.948459875572344), R = (-2.222222222222222, -1.283000598199168, 1.134023029066286), S = (0, 0, 4.762896722078402), T = (0, 0, -0.680413817439772), U = (1.6666666666666667, 0.962250448649377, 0.680413817439772), V = (0, 1.924500897298753, 3.402069087198859), W = (-1.6666666666666667, 0.962250448649376, 0.680413817439772), Z = (1.6666666666666667, -0.962250448649377, 3.402069087198859 ), A1 = (0, -1.924500897298753, 0.680413817439772), B1 = (-1.6666666666666667, -0.962250448649376, 3.402069087198859). This three-dimensional polytope was discovered by the Dominican Jose Joel Leonardo on January 4, 2020 at 8:18 pm and was named by its author on January 16, 2021 in honor of the Queen of England Isabel II. The first 12 points define an Archimedean cuboctahedron (from point A, to point L). The remaining 14 points define the midpoints of each of the faces that form the cuboctahedron (from point M to point B1) and with the combination of these fourteen points we form the Queen Isabel II Octahedral Star.Français : C'est un solide tridimensionnel concave, composé de 24 triangles isocèles de Jose uniformes entre eux, 14 sommets et 36 arêtes déformées. Le polyèdre dual de ce solide est le cuboctaèdre.
14 sommets sont répartis en: huit sommets extérieurs qui sont communs aux trois triangles isocèles Jose (M = (2,222222222222222, 1,283000598199168, 2,948459875572344), N = (0, 2,566001196398337, 1,134023029066286), O = (2,222222222222222, -1,283000598199168, 1,134023029066286), P = (0, -2,566001196398337, 2,948459875572344), Q = (-2,222222222222222, 1,283000598199168, 2,948459875572344), R = (-2,222222222222222, -1,283000598199168, 1,134023029066286), S = (0, 0, 4,762896722078402), T = (0, 0, -0.680413817439772)) et six sommets intermédiaires où huit triangles isocèles convergent dans chaque Jose (U = (1,6666666666666667, ,962250448649377, ,680413817439772), V = (0, 1,924500897298753, 3,402069087198859), W = (-1,6666666666666667, ,962250448649376, ,680413817439772), Z = (1,6666666666666667, -0,962250448649377, 3,402069087198859) A1 = (0, -1,924500897298753, ,680413817439772), B1 = (-1,6666666666666667, -0,962250448649376, 3,402069087198859)). Les 36 arêtes sont réparties en douze arêtes intermédiaires et 24 arêtes externes en étoile. Les bords intermédiaires de ce polyèdre sont plus grands que les bords étoilés extérieurs. La dualité entre la octaédrique Star Queen Isabel II et cuboctaèdre est démontré dans la définition de ces 26 points géométriques A = (1,6666666666666667, ,962250448649376, 4,762896722078402), B = (1,6666666666666667, 2,886751345948129, 2,041241452319315), C = (-1,6666666666666667, 2,886751345948129, 2,041241452319315), D = (3,3333333333333335, 0, 2,041241452319315), E = (0, -1,924500897298752, 4,762896722078402), F = (1,6666666666666667, -2,886751345948129, 2,041241452319315), G = (-1,6666666666666667, -2,886751345948129, 2,041241452319315), H = (-1,6666666666666667, ,962250448649376, 4,762896722078402), i = (-3,3333333333333335, 0, 2,041241452319315), J = (0, 1,924500897298753, -0,680413817439772), K = (-1,6666666666666667, -0,962250448649376, -0,680413817439772), L = (1,6666666666666667, - ,962250448649376, -0,680413817439772 ), M = (2,222222222222222, 1,283000598199168, 2,948459875572344), N = (0, 2,566001196398337, 1,134023029066286), O = (2,222222222222222, -10 199168, 1,134023029066286), P = (0, -2,566001196398337, 2,948459875572344), Q = (-2,222222222222222, 1,283000598199168, 2,948459875572344), R = (-2,222222222222222, -1,283000598199168, 1,134023029066286), S = (0, 0, 4,762896722078402), T = (0, 0, -0,680413817439772), U = (1,6666666666666667, ,962250448649377, ,680413817439772), V = (0, 1,924500897298753, 3,402069087198859), W = (-1,6666666666666667, ,962250448649376, ,680413817439772), Z = (1,6666666666666667, -0,962250448649377, 3,402069087198859 ), A1 = (0, -1,924500897298753, 0,680413817439772), B1 = (-1,6666666666666667, -0,962250448649376, 3,402069087198859). Ce polytope tridimensionnel a été découvert par le dominicain José Joel Leonardo le 4 janvier 2020 à 20h18 et nommé par son auteur le 16 janvier 2021 en l'honneur de la reine d'Angleterre Isabel II. Les 12 premiers points définissent un cuboctaèdre d'Archimède (du point A au point L). Les 14 points restants définissent les points médians de chacune des faces qui forment le cuboctaèdre (du point M au point B1) et avec la combinaison de ces quatorze points, nous formons l'étoile octaédrique Queen Isabel II. |
Date | |
Source | Own work |
Author | Jose J. Leonard |
File:Clasificación_De_Triángulos_Según_Sus_Lados.jpg https://commons.wikimedia.org/wiki/File:Clasificaci%C3%B3n_De_Tri%C3%A1ngulo_Is%C3%B3sceles.gif File:Poliedro_Estrellado.jpg
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