observe a polyhedron ; in its top must converge at least three faces that are not on the same plane (otherwise there would be no cusp and faces WOULD BE on the same floor), then the sum of their angles must be less than 360 °.
Every corner of an equilateral triangle measures 60 °: it is therefore possible to meet at a summit three equilateral triangles (3 x 60 ° = 180 °) to obtain a regular tetrahedron :
Every corner of a square measures 90 °: it is therefore possible to see in a Summit 3 (no more: with 4 h around the corner!) square faces (3 x 90 ° = 270 °) to obtain un cubo .
Il cubo:
Con 4 facce triangolari (triangoli equilateri, 4 x 60° = 240°) ottengo un ottaedro regolare .
L'ottaedro:
Ogni angolo di un pentagono regolare misura 108°. E' quindi possibile far incontrare in un vertice un massimo di 3 facce pentagonali regolari (3 x 108° = 324°) ottenendo un dodecaedro regolare .
Il dodecaedro regolare ha per facce dei pentagoni regolari che si incontrano in ogni vertice a tre a tre:
Con 5 facce (triangoli equilateri, 5 x 60° = 300°) ottengo un icosaedro regolare . I can not have more than 6 equilateral triangles for 60 ° x6 = 360 °, and then I turn the corner: the faces WOULD BE on the same plane.
The regular icosahedron has 20 equilateral triangles for faces:
And with regular hexagonal faces I could build a solid? Every corner of a regular hexagon is 120 ° and then if 3 sides meet in a summit would be on the same level (3 x 120 ° = 360 °). I can not build a solid !
Look for developments in the plane of the solids go here.
0 comments:
Post a Comment