MATHEMATICS AND ORIGAMI
Jesús de la Peña Hernández 18.9 OCTAHEDRON C = 8 ; V = 6 ; A = 12 18.9.1 Bipyramidal OCTAEDRON 18.9.2 Wound up OCTAHEDRON Start ...
Mathematics and Origami 18.9.4 OCTAHEDRON made of two interlocked domes Start with a square (Fig. 1) and divide the perigon at O ...
Jesús de la Peña Hernández 18.9.5 Skeletonlike OCTAHEDRON Folding angle of profile 3 is 109,47123º, twice as much as angle α in ...
Mathematics and Origami 3- All the diagonals will be mountain fold except those affected by a module change (see later). Therefo ...
Jesús de la Peña Hernández 9- To continue with a second module, turn over the strip twice on a pair of succes- sive diagonals. W ...
Mathematics and Origami 18.12 STELLATE REGULAR POLIHEDRA To try to explain them we shall apply to the stellate polygons (Point11 ...
Jesús de la Peña Hernández HD= OH^2 +OD^2 = 1 , 4142135 L (curiously HD = 2)L BD=DC= 0 , 618034 L (equal value than AC ́, Point ...
Mathematics and Origami As we can note, the auxiliary dodecahedron has enable us to draw Figs. 1, 2, 3, 4 but it does not allow ...
Jesús de la Peña Hernández Let ́s compute the faces. From each vertex start 5 equilateral triangles common, in turn, to 3 vertic ...
Mathematics and Origami 18.12.2 STELLATE REGULAR POLYHEDRON nº 2 The auxiliary starting polyhedron is, in this case, a convex ic ...
Jesús de la Peña Hernández The faces are planes concurrent in the vertices, i.e. convex pentagons. These pentagons have species ...
Mathematics and Origami The species ε according to Euler is: 3 2 12 2 1 12 30 2 = × + × − = + − = Ce EV A ε To resume: polyhedro ...
Jesús de la Peña Hernández This means that the pyramid ́s lateral side HB has equal length than the pentagon ́s di- agonal B ́C ...
Mathematics and Origami Finally we get polihedron nº 4 as shown in Fig. 4. To draw it we have used a very sim- ple contrivance: ...
Jesús de la Peña Hernández 18.13 PSEUDORREGULAR POLIHEDRA All their faces are equal (as in the regular polyhedra), or symmetrica ...
Mathematics and Origami To figure out that angle, let ́s set up first the hypothesis that a rhombic face has L as the great diag ...
Jesús de la Peña Hernández If we assume that the dimension of a rhomb ́s small diagonal is 1, the great will measure 2 and the s ...
Mathematics and Origami TRAPEZOHEDRON It is a pseudorregular polyhedron with 24 trapezoid shaped faces, 26 vertices and 48 sides ...
Jesús de la Peña Hernández 2 1 2 = = = = AB AC CD DA Thus we have settled ∆CDI which is homothetic to ∆EFG. Let ́s find now the ...
Mathematics and Origami 18.14 MACLES In crystallography are so named the twinned crystals oriented in such a way that one can ov ...
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