File:Icosaedro de Jose.gif
Icosaedro_de_Jose.gif (646 × 315 pixels, file size: 1.72 MB, MIME type: image/gif, looped, 200 frames, 16 s)
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Español: Los icosaedros de caras uniformes se clasifican en tres, los cuales son: a)Icosaedro de Leonardo ampliado o icosaedro de Joel: este está compuesto por 20 triángulos isósceles de Joel, los cuales son uniformes entre sí, 20 aristas mayores uniformes, 10 aristas menores uniformes y 12 vértices intermedios. b)Icosaedro regular o icosaedro Platónico: posee 20 triángulos equiláteros uniformes, 30 aristas uniformes y 12 vértices uniformes. c) icosaedro de Leonardo disminuido o Icosaedro de Jose, este está compuesto por 20 triángulos isósceles de Jose los cuales son uniformes, 20 aristas menores uniformes, 10 aristas mayores uniformes y 12 vértices intermedios. Este solido geométrico, pertenece al conjunto de poliedros que poseen todas sus caras irregulares uniformes, entre los cuales podemos mencionar los 13 poliedros de catalán.
Triángulo isósceles menor o triangulo isósceles de Jose: es aquel triangulo cuyos dos lados iguales llamados patas son de menor medida, que el lado desigual llamado base. Este símbolo (<) representa la palabra menor que. Este símbolo numérico conocido como tres (3) representa la palabra triangulo. Este símbolo literal conocido como (s) representa la palabra isósceles. El triángulo isósceles de Jose o triangulo isósceles menor es representado por: 3s<. El ángulo que forma uno de los dos lados llamado pata de un triángulo de Jose, con el lado llamado base, siempre es menor de sesentas grados. El ángulo que forma uno de los dos lados llamado pata de un triángulo isósceles, con el lado llamado base, siempre es mayor o menor de sesentas grados, pero no puede ser igual a sesentas grados. 3s> 60, 3s<60, pero 3s no igual a 60. En el momento que una de las dos patas iguales de un triángulo miden sesentas grados, con el lado llamado base, en ese preciso instante el triángulo se ha transformado en un triángulo equilátero. 15 de abril 2012 fue descubierto este poliedro por el profesor Jose Joel Leonardo. Si aplicamos la fórmula de Euler en el icosaedro de Leonardo disminuido: C = caras, A = aristas, V = vértices. Formula de Euler: A=C+V-2. C=20, V=12, A=30. Sustituyendo: A=C+V-2, 30= 20+12-2, 30=30, hemos verificado la igualdad de la formula, por lo tanto la formula se cumple.English: Icosahedrons with uniform faces are classified into three, which are: a) Leonardo's Icosahedron enlarged or Joel's icosahedron: this is composed of 20 isosceles Joel triangles, which are uniform among themselves, 20 uniform major edges, 10 minor edges uniform and 12 intermediate vertices. b) Regular icosahedron or Platonic icosahedron: it has 20 uniform equilateral triangles, 30 uniform edges and 12 uniform vertices. c) icosahedron of Leonardo diminished or Icosahedron of Jose, this is composed of 20 isosceles triangles of Jose which are uniform, 20 uniform minor edges, 10 uniform major edges and 12 intermediate vertices. This geometric solid belongs to the set of polyhedra that have all their uniform irregular faces, among which we can mention the 13 Catalan polyhedra.
Isosceles minor triangle or Jose's isosceles triangle: is that triangle whose two equal sides called legs are of lesser measure, than the unequal side called base. This symbol (<) represents the word less than. This numerical symbol known as three (3) represents the word triangle. This literal symbol known as (s) represents the word isosceles. Jose's isosceles triangle or minor isosceles triangle is represented by: 3s <. The angle formed by one of the two sides called the leg of a Jose triangle, with the side called the base, is always less than sixty degrees. The angle formed by one of the two sides called the leg of an isosceles triangle, with the side called the base, is always greater or less than sixty degrees, but it cannot be equal to sixty degrees. 3s> 60, 3s <60, but 3s not equal to 60. At the moment that one of the two equal legs of a triangle measures sixty degrees, with the side called the base, at that precise moment the triangle has become an equilateral triangle. April 15, 2012 this polyhedron was discovered by Professor Jose Joel Leonardo. If we apply Euler's formula on Leonardo's diminished icosahedron: C = faces, A = edges, V = vertices. Euler's formula: A = C + V-2. C = 20, V = 12, A = 30. Substituting: A = C + V-2, 30 = 20 + 12-2, 30 = 30, we have verified the equality of the formula, therefore the formula is fulfilled. |
| Date | |
| Source | Own work |
| Author | Jose J. Leonard |
https://commons.wikimedia.org/wiki/File:Icosaedro_De_Leonardo.gif https://www.geogebra.org/m/st9ywbbe
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