File:Tetraedro de Pacheco.gif

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Tetraedro_de_Pacheco.gif ‎(677 × 553 pixels, file size: 3.3 MB, MIME type: image/gif, looped, 189 frames, 16 s)

Captions

Captions

Tetrakis hexahedron: It is a convex three-dimensional polytope, which has 24 uniform scalene triangles, 14 deformed vertices and 36 deformed edges.

Summary

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Description
Español: Tetraedro de Pacheco: Es politopo tridimensional convexo, que posee 24 triángulos escaleno uniforme, 14 vértices deformes y 36 aristas deformes. 
Este poliedro si hubiera sido descubierto por el matemático Belga, Eugéne Charles Catalán, hoy ocuparía la tercera posición de sus  poliedros.

Si le aplicamos al tetraedro de Pacheco, la fórmula de poliedro de Euler: C+V-2= A, C=24, V=14; sustituyendo en la fórmula: C+V-2=A, 24+14-2=A, 36=A. Vemos que se cumple.

COORDENADAS CARTESIANA DEL TETRAEDRO DE PACHECO.

Las siguientes coordenadas cartesiana definen un tetraedro de pacheco centralizado: A (0.001579046836937,0, 6.124216179730865), B (-2.885172299111192, 5, -2.040749629546396), C (-2.885172299111192, -5, -2.040749629546396), D (5.775081738733194, 0, -2.040749629546396), E (-1.565677732757272, 2.714568370763947, 2.21692761619623), F (-1.565677732757272, -2.714568370763947, 2.21692761619623), G (3.136092606025354, 0, 2.21692761619623), H (1.565677732757272, 2.714568370763947, -2.21692761619623), I (1.565677732757272, -2.714568370763947,- 2.21692761619623), J (-3.136092606025354, 0, -2.21692761619623), K (1.628115928429037, 2.81724451930216, 1.150627081596715), L (1.628115928429037, -2.81724451930216, 1.150627081596715), M (-3.251494716347263, 0, 1.150627081596715),N (0, 0, -3.449913068993375)

El tetraedro de Pacheco, pertenece al conjunto los poliedros que poseen caras triangulares, ocupando la posición #11 (L=29, A=3L+3, V=L+3 y C=2L+2), de acuerdo a las formulas sucesiones poliédricas triangulares del Leonardo.

HISTORIA: Este poliedro fue descubierto el 5 de enero del año 2021 por el matemático Dominicano Jose Joel Leonardo.

A la 12: 35 de a madrugada del 11 de enero del 2021, el descubridor de este politopo tridimensional lo nombro con el nombre de tetraedro de Pacheco, en honor un político y filántropo dominicano llamado Alfredo Pacheco Osoria.
English: Pacheco tetrahedron: It is a convex three-dimensional polytope, which has 24 uniform scalene triangles, 14 deformed vertices and 36 deformed edges. 
If this polyhedron had been discovered by the Belgian mathematician, Eugéne Charles Catalán, today it would occupy the third position of his polyhedra.

If we apply to Pacheco's tetrahedron, Euler's polyhedron formula: C + V-2 = A, C = 24, V = 14; substituting in the formula: C + V-2 = A, 24 + 14-2 = A, 36 = A. We see that it is fulfilled.

CARTESIAN COORDINATES OF THE TETRAHEDRO OF PACHECO.

The following Cartesian coordinates define a centralized Pacheco tetrahedron: A (0.001579046836937,0, 6.124216179730865), B (-2.885172299111192, 5, -2.040749629546396), C (-2.885172299111192, -5, -2.040749629546396), D 2.040749629546396), E (-1.565677732757272, 2.714568370763947, 2.21692761619623), F (-1.565677732757272, -2.714568370763947, 2.21692761619623), G (3.136092606025354, 0, 2.21692761619623), H (1.565677732757272, 2.714568370763947, -2.21692761619623), I (1.565677732757272, -2.714568370763947, - 2.21692761619623), J (-3.136092606025354, 0, -2.21692761619623), K (1.628115928429037, 2.81724451930216, 1.150627081596715), L (1.628115928429037, -2.81724451930216, 1.150619623, 016724451930216, 1.1341562708), M -3.449913068993375)

The Pacheco tetrahedron belongs to the set of polyhedra that have triangular faces, occupying position # 11 (L = 29, A = 3L + 3, V = L + 3 and C = 2L + 2), according to the succession formulas triangular polyhedral of the Leonardo.

HISTORY: This polyhedron was discovered on January 5, 2021 by the Dominican mathematician Jose Joel Leonardo.

At 12:35 a.m. at dawn on January 11, 2021, the discoverer of this three-dimensional polytope named it the Pacheco tetrahedron, in honor of a Dominican politician and philanthropist named Alfredo Pacheco Osoria.
Français : Pacheco tétraèdre: C'est un polytope tridimensionnel convexe, qui a 24 triangles scalènes uniformes, 14 sommets déformés et 36 arêtes déformées. 
Si ce polyèdre avait été découvert par le mathématicien belge Eugéne Charles Catalán, il occuperait aujourd'hui la troisième position de ses polyèdres.

Si nous appliquons au tétraèdre de Pacheco, la formule du polyèdre d'Euler: C + V-2 = A, C = 24, V = 14; en remplaçant dans la formule: C + V-2 = A, 24 + 14-2 = A, 36 = A. Nous voyons qu'il est accompli.

COORDONNÉES CARTESIENNE DU TETRAHEDRO DE PACHECO.

Les coordonnées cartésiennes suivantes définissent un tétraèdre Pacheco centralisé: A (0,001579046836937,0, 6,124216179730865), B (-2,885172299111192, 5, -2,040749629546396), C (-2,885172299111192, -5, -2,040749629546396), D 2,040749629546396), E (-1,565677732757272, 2,714568370763947, 2,21692761619623), F (-1,565677732757272, -2,714568370763947, 2,21692761619623), G (3,136092606025354, 0, 2,21692761619623), H (1,565677732757272, 2,714568370763947, -2,21692761619623), I (1,565677732757272, -2,714568370763947, - 2.21692761619623), J (-3.136092606025354, 0, -2.21692761619623), K (1.628115928429037, 2.81724451930216, 1.150627081596715), L (1.628115928429037, -2.81724451930216, 1.13021623 M, 1.130216246, 1.13021623 -3,449913068993375)

Le tétraèdre de Pacheco appartient à l'ensemble des polyèdres à faces triangulaires, occupant la position # 11 (L = 29, A = 3L + 3, V = L + 3 et C = 2L + 2), selon les formules de succession polyédrique triangulaire du Leonardo.

HISTOIRE: Ce polyèdre a été découvert le 5 janvier 2021 par le mathématicien dominicain Jose Joel Leonardo.

À 12 h 35 le 11 janvier 2021, le découvreur de ce polytope tridimensionnel l'a baptisé tétraèdre Pacheco, en l'honneur d'un politicien et philanthrope dominicain nommé Alfredo Pacheco Osoria.
Date
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Author Jose J. Leonard

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